lol I feel your pain! I do the school run, since I have my older 2 currently in JK and SK, plus 1 dck in SK as well. In the spring it's great, the weather is nice, the kids love having a destination, etc, but in the winter, it's horrible. And the school is only next door, not even a five minute walk! In 2 feet of snow pushing a double or triple stroller though, it feels like an hour! Your thinking is not terrible at all!
Congrats on getting into the program, it'll save you a huge headache!