CC'ing or OC'ing in National Forest

I am pretty sure I have read that no firearms are allowing in National Forests. One in particular I would like to know is up Mirror Lake Hwy. I went camping there this year and still brought my gun. Though it stayed in the truck until night time. I put it on my persons at night and had it by me during bed time to protect my family. I know you can legally have it in your tent because it is your temporary housing. But the main question is can I have it on me outside of my tent during the day. We did see bears during camping an would like to have self protection. Though I wouldn't use it unless the bear started after me.

Thanks in advance.

Josh