I too use to be a weather whimp.
Under 70- not riding.
Wind blowing above 10 mph- not riding
Rain- not riding
The way I got over it, was signing up for a Tri 101 program that started in February. I refused to miss my workouts, because I paid for it. So, this year... I have ridden on the coldest day of the year... I have fought 25-30 mph headwinds.
I still REFUSE to ride in the RAIN though. I just think that's dangerous.
Even though won't need to, I might join the Tri 101 program again next February. All that training early in the season helped me get out the door, and prepared for the MS150 in May.
"Life is not a journey to the grave with the intention of arriving safely in a pretty and well preserved body, but rather, to skid in broadside thoroughly used-up, totally worn out, and loudly proclaiming: WOW WHAT A RIDE!!!!"