Need travel tips using carry on luggage

We have done a couple of 2 weeklong Europe trips with only a carry on. Can you do laundry while there? That will definitely help. We packed 4 pairs of pants, 5 tops that we could make multiple outfits with. Select a color scheme that allows you to mix and match outfit pieces. Don't pick a pair of pants or a top that will only go with one thing. Mixing outfits up will help, plus you won't look like you wore the same thing every day. Try light fabrics that travel well. Merino wool tops or travel pants that don't wrinkle. Only 1 pair of gloves, hat and scarf that will match your color scheme.
For your toiletries, you only need one lipstick, one eyeshadow palette, etc. Now isn't the time to switch up your makeup colors. Keep it simple. Do you flat iron your hair? I brought a travel sized Baby Bliss flat iron that worked well overseas.

If you only plan to use an item once or twice, you don't need it. Leave it at home. It really helps me to go through my suitcase and backpack more than once and ask myself how often I will use that item. That helps me to downsize. In Europe, you will find yourself having to climb stairs, deal with narrow passageways, etc. Traveling light really made our trip more enjoyable. If you can squeeze in a duffle bag, you can transfer dirty clothes to that and check that bag on the way home. That will free up luggage space for any of your purchases. I hope you have a great trip!

First of all I would encourage you to rethink how much makeup, hair, and "face stuff" you're planning to take. 

For a coat, find a down (or the fake down which can be just as warm, at least for ordinary purposes) one that's light enough to carry and that's squishable enough that you could smoosh it into a corner of your carry on. But plan to wear it onto the plane. 

Definitely go for mix and match, with only a basic color scheme. Dark bottoms, with lighter tops. Take a couple of cardigan-type items that are the same color as the pants so they can be worn with any of the tops. -- Rather than taking any bulky sweaters, bring a thin under layer like a cami. -- Don't worry about "oh everyone will see me in the same outfit". Even if you're with the same people for the entire trip they don't care. They've packed the same way so they're wearing the same clothes again also. And none of the locals will know because you'll be visiting different places anyway.  

Personally I like the packing cubes although you'll get varying opinions about them. If you're going to one hotel and are going to stay there then the cubes might not be as useful. But if you're doing a trip where you'll be staying in multiple locations they can be a sanity saver. Dd and I went to Israel for two weeks using only carry-ons, and we used the packing cubes. We changed hotels every two days so we never unpacked. And it was lovely to open our suitcases and see all the cube organization. lol

Pack some sort of tote bag... there are a lot of them that will fold up into a very small package. Coming home you can check your bag and use the tote for souvenirs that you don't want to risk getting lost. 

Make sure that any important medications, electronics, etc. are in your personal item (i.e., your purse or whatever bag is standing in for that) not in your carry-on, just in case you have to gate-check the carry-on.

Definitely start early with your packing. If you wait you will panic pack and add unnecessary things.
Layout your clothes to make sure everything goes with everything else.
I wouldn't pack more than 2 pairs of pants plus the pair I wear on the plane.
Look into a wool tank or 2 as an under layer.
Consider cashmere as your sweater choice, its very warm, yet light weight.
Bring laundry sheets to do underpants and socks in your room, be sure to roll up any washed items in a towel to squeeze out excess moisture before setting out to dry.
Maximize your under seat bag size and pick one that can be attached to your roller bag if that is what you are using.
Another suitcase option is this Rick Steve's bag Unexpanded it is carryon size. If you pick up too many things, it expands quite a bit and then you can check it on your way home. It is a back pack style with comfortable straps and waist band.
Really think about what you will be doing and your shoe choices. I am in So Cal and typically only travel to Europe in winter. I wear Chelsea boots practically everyday. I do pack an extra pair of shoes.
I find it easier to break down my bathroom bag into smaller bags rather than trying to pack around a large bathroom bag. And remember to check your husbands bathroom bag for redundancy.
I am a fan of packing cubes. However for carryon only, I don't put everything into packing cubes because I am trying to maximize every bit of space.

Have fun!

Agree with limiting the amount of cosmetics and hair products you bring, not only to save space, but because of TSA limits for liquids and aerosols in carry on bags. Some things I've done to help with that are to switch to bar shampoo, conditioner, and soap, and to incorporate powder cosmetics as much as possible. Or simply go without makeup - as others have said, no one cares. You can throw in mascara and a lipstick for an evening out if you want.

Consider putting together a capsule wardrobe where everything goes together and you can wear the same two pairs of shoes with all of it. If your accommodations will have washing facilities, you can plan to use them if necessary, but be aware that dryers outside of the US usually don't dry things the way we expect, and you will need to leave enough time for things to drip-dry.

If you are going to be re-wearing things, I suggest hanging them up to air out when you are in one place instead of re-packing them or putting them in drawers. Even clothes that don't smell after you wear them develop that "dirty laundry" smell when bunched up all together. Doesn't bother everyone, but it does me.

As others have said, prioritize comfort and convenience over looking cute and put together. No one will bat an eye at yoga pants and sneakers, even in Europe.

Roll everything
Bring a basic black or gray dress that you can pair with leggings and boots
Bring a variety of leggings and a sweater to dress up the dress, can include your scarf
Wear comfortable boots
Bring slippers and one pair of pajamas
Bring a plastic bag to put your worn underwear and socks in
Wear wool socks, they don't get stinky like others. You can bring less pairs
Streamline your makeup as much as possible
Bring makeup remover wipes
Travel size shampoo and conditioner are not optional for me! And I include a small brush for drying, plus a straightener, though if I was in a pinch I could go with a scrunchie and keep my hair up or in a hat every day
One pair of pants or jeans with a sweater or T-shirt or long sleeved shirt

Those are my basics.
I can get all that plus my meds in just my backpack (considering I'm wearing some of it) but that's a little less than I prefer to bring. There is more room in my carry-on so I can include more choices.
And I inevitably end up buying a shirt or t shirt or sweatpants every place I visit, because I'm touristy like that.

If it was winter I would have 3 pairs of shoes: Chelsea black boots (would wear on plane), sneakers, and heels.

I’d wear black leggings every day. Can dress them up or down.
I’d have a couple flirty skirts for evenings.
One jacket in cream or black that also can be dressed up or down.
I think I could do it…