Yes, you need them.  The glare off the snow can harm your eyes just as the sun in the warm, summer months can.  You should always wear sunglasses to protect your eyes if the sun is out enough to cause you to squint or strain your eyes at all.  Mine automatically adjust to the level of light so they’re always with me.  I’m trying to avoid further eye damage (I don’t want to wear coke bottles for glasses) as well as wrinkles.  The closer you get to middle-age, the more you start to worry about things like this.  Believe me. 

When you’re young, you think nothing bad can happen.  The damage you do to your eyes when you are young can and will affect your vision as you age.  Take care of what you have.