If you've got snow in your area, go sledding. Usually there are a lot of other people around so it will be safe.  You will really get to know your date and have many laughs. Ice skating is an inexpensive date to partake in. If one of you has never ice skated, all the better!  You can teach your date. If live in an area where you've got plenty of snow on the ground, building a snowman is a lot of fun and no pressure.  Don't forget to  make snow angels too!

 If you have the holiday tradition of Christmas trees, ask your date to go with you to choose one.  Or if you cut them down yourself, that works too. If you celebrate Christmas and have some Christmas shopping to do, invite your date with you.  Be sure to ask what they think of things you are buying.  You'll get to see what they like and don't like.  For those sports enthusiasts, check out a local hockey game, even if it's just the local high school team. Hockey games are generally exciting and a lot of fun. Go for hot chocolate afterwards, or bring some with you as it will be chilly even if it is indoors.