I know the wrap stayed on the car when I swapped batteries. It is insulated. I would get one if it's not too expensive.
On the towing thing, it's hard to beat an AAA membership for like $69 a year. Tows, starts, pump up your tire, gallon of gas, open your door is nice to have. Plus, you can get discounts for motels, even NAPA Auto Parts.
97 T-Bird LX 4.6 - 68k miles
94 Supra TT Auto - street/strip car
04 Crown Vic Police Interceptor - Brenda's car
95 T-Bird LX 4.6 - fully optioned, owned 15 years
96 Cougar XR-7 4.6- Brenda's car, owned 11 years
88 T-Bird 3.8 - first T-Bird, owned 5 years