You are riding too far too soon. Ride by time, not distance. Start with maybe a 10minute ride and extend by about 5 mins each time. Don't ride too hard, you need to become conditioned to riding before you use it for fitness. Take a week or two just to settle into the bike.
I reckon on a newbie taking about 3 weeks to feel at ease on a bike and about 3 months to become fully conditioned to the point where you can ride all day without discomfort. This has little to do with strength or fitness or riding fast, that is another thing altogether and Im not qualified to comment.
Depending on your climate, you can ride quite a way through the winter. Ice and snow are tricky but plain old rain and wet roads shouldn't stop you as long as you are prepared. You have to dress for the weather so see the stickies in Winter riding forum.