I've had much the same experience in my unheated garage for the last 17 years. The coldest it has gotten in my garage is 10F. It takes about 2 minutes for the bulbs to fully brighten when that cold. As I recall the ballasts were rated at -10F.I bought a cold start rated T8 twin tube 4ft fluorescent shoplight for my garage about 6yrs ago from Lowes or Home Depot (don't recall).
I was just out in the garage and it's 0degF out. It fires up to full brightness. No need for special bulbs. It's all in the ballast for T8s.