For Ochako's birthday and Christmas, she will find a star projector wrapped horribly in his best effort for Christmas and birthday. Half of the present is in one theme, the other is in the other theme because he couldn't decide which one he should do over the other. There is a tag on it that says

Merry Christmas and Early Happy Birthday
- Shoto Todoroki

For New Years there is a text on her device the next time she looks at their messages or messages in general.

Hello Uraraka.

Happy New Year and I hope the upcoming one will be good. I know we're far from home, but we have been on away missions before. There is a reason for everything and I believe that, strongly. In the new year, all four of us should do something fun together. I would like to take the time we have away from everything back home to know everyone even better. I hope you feel the same.

- Shoto

Yes he signed his own text. It's a letter after all.