Aang-
Aang likes making chilly winter breezes randomly to startle you, then he acts completely innocent about it. He also does this with the others too, but it's most often with you. Aang's gifts are simple, but cool. He's the kind of gifter that remembers what people need and gets that for them, though he is always happy to take suggestions, preferably before Cyber Monday so he doesn't second-guess himself and stress about it. Aang likes to decorate his staff with Christmas lights and gets friends to hook it up so it has it's own power source. All the kids find it cool, especially at night, you do too but your worried that it may make Aang a target. Well he is, being the avatar, but more so. He's super determined to see the lights through the month though, and you know nothing you say can get through to him at that point. Since you guys are on the run you don't really have your own Christmas tree, but he is always happy to help different towns get their giant star up before the Christmas Tree Lighting. His favorite Christmas activity is probably wrapping, even though he isn't that good at it, he's still super proud of his wrapped gifts and gets super excited when you offer to give him some pointers. The whole Gaang wakes up slightly earlier in order to exchange gifts while Katara makes a slightly better breakfast to mark the occasion. Aang likes ripping into the wrapping paper before remembering that wrapping paper is super expensive and neatly takes off the wrapping paper for the rest. You guys stop traveling early in order to play in the snow and do other leisurely activities.
Sokka-
Sokka likes building super complicated snow forts, though they never really work out like he wanted them to. He procrastinates getting everyone's gifts after the Black Friday rush, if he has anything left to get. Then when you bother him he's just like 'relax, I'll just whittle something' then last minute he's scrambling around and your just like 'told ya' while reading a newspaper or something. Sokka goes all out for Christmas, wearing anything and everything Christmassy, he and Aang even made this move where Aang brins him super high up before dropping on his enemies while shouting 'Ho Ho How Hurt Are You Attack!!' It's way too funny. You guys may not have a tree but Sokka will whittle little ornaments for nearby pine trees, but he has to stop because the Fire Nation may find them because of it. But he still sneaks one on a tree every once in awhile. His favorite Christmas activity is chugging hot chocolate like there's no tomorrow, he wants to see if he can increase his record every year. Even if it's by a half-mug. Sokka totally wakes up super early on Christmas and waits for everyone patiently so he can start opening presents. He gets so excited and doesn't care about saving the wrapping paper, he just rips it off out of excitement to see what's inside. You guys actually don't go anywhere and stay in one place, so you all have snowman look alike competition. Yours ends up winning the contest and while Sokka is proud of you his ego took a huge hit so expect lots of cuddles.
Zuko-
Zuko, like Halloween, loves the being with family and having fun aspect. Ever since his Mom left Christmas just wasn't the same and he gets so excited to celebrate it with the ones he cares about. In fact he's so excited he gets all of the presents super in advance, like in September. Everyone but Toph has an idea of what they're getting, since she can't see. But she knows the general shape and weight of all the gifts combined. You see this crappy pair of reindeer horns and jokingly tell Zuko he should wear it for the whole December month. He takes this seriously and actually buys them and wears them. He also gets these ridiculous red pom-poms for the hilt of his swords too, it's stupid but it's better than Sokka and Aang's 'Ho Ho How Hurt Are You Attack'. You guys don't have a tree per say but you draw one and everyone gets to add their own little ornaments to it, you let Zuko draw the star and he feels so blessed tho. It's almost like he's putting the real one up. His favorite thing to do is help you bake cookies with his fire bending. It's also a great way to teach Aang about temperature control. Your cookies are always the best and everyone wants some. Though they have to pitch in to decorate them with frosting. Except for Toph, she gets to do sprinkles and candy bits on the cookies. She's surprisingly good at it. Zuko gets up super early and wakes up about five minutes after Sokka and keeps him from opening the presents too early. Which are 'guarded' by Appa. Zuko is a careful gift opener, after years of being told to by his Father, he also remembers to save it for next year in case if the war isn't over. You guys kinda spend the whole day leaning against Appa, cuddling under a super warm blanket with some eggnog and talking while saying 'I love you' with little nose kisses and a ton of giggling. It's really nice.
Jet-
Jet likes the candy canes that you can get only during Christmas, and steals a crap ton from the fire nation just so he could have it in his mouth instead of his usual piece of grass. He's the kind of person who would make the candy cane ends sharp to stab people with then have this belt of sharp-ass candy canes and actually stab people with them. For presents he either whittles people a little something or regifts something he stole from the fire nation troops. But let's be honest, everyone does that. You have this really small tree and you put the same ornaments in the same places every year. Not that you guys mind. His favorite thing to do is do his bomb santa impression when you raid a camp and literally half the guys go 'oh my god! Saannnnttttaaa!' Then one guy's like 'wait, isn't it too-' boom, stabbed by a candy cane. One time they all freaked out and were like 'we're on the naughty list!!' and just ran around screaming before running away from the camp. Their reactions are always hilarious. Jet wakes up super early on Christmas day, not so he could see what he got, but to keep the others from opening their presents. He's super careful opening them because wrapping paper and newspaper is expensive. Then he just goes back into the hut to sleep and drags you along so he can cuddle with you. If he doesn't sleep the whole day you guys would totally have a snowball fight with the other freedom fighters.