Just because it's cold outside doesn't mean you can't have a great outdoor date. Winter weather brings on a whole different set of fun activities that you can't do during the three other seasons of the year. This fact alone makes an outdoor winter date a little more unique and memorable, and this will mask the fact that you're not paying anything to have fun together. Besides, if she gets cold, she'll need a hug to warm up.
Right after you get a heavy snowfall, suggest building a snowman. Try to make one as big as possible--and if it escalates into a little snowball fight, that's fun too.
If there's enough snow on the ground, hit the hills for sledding or tubing. Sharing the same sled will give you an excuse to be close.
Snowshoeing is another great outdoor activity. It's a lot like hiking, which means you'll be able to enjoy the beauty of the woods without worrying about trudging through a lot of snow.
Need another winter idea? Go ice-skating. Even if neither of you is a strong skater, ice-skating is still a fun date activity because you can develop a bond by supporting each other as you try not to fall on the ice.