Not
many of us are going to point fingers at you and laugh, just because you're trying to ride a road bike as a commuter or because you wimped out when confronted by a bit of water. (JK,
)
Commute on any bike you want, as much or as little as you feel like doing, do it because you enjoy it and the benefits (as you pointed out) you receive because of it. You may find, as others here have, that you'll get the bug to commute frequently, even daily, even year round and may have to get a bike for the days that you don't want to take your baby out.