I know my tomato plants have gone crazy with all the rain we've gotten. I've been a little worried about how cold its been, but I had tons of flowers last night when I watered, so they seem happy enough.

Yes, mine are definitely happy, though the tissues are so water-filled they break easily. I've found it's wiser not to mess around with trying to arrange the branches right after rain, even though that's the time they seem to require tying or tucking up. The branches are more flexible when the tissues aren't full of water.

I'm just wondering if anybody knows if lots of rain early in a tomato's life (that results in rapid fruit expansion) affects the taste or texture later.

We are getting copious amounts here too and live with the daily Flood Watch Warning. But too much rain only affects fruit that is past breaker stage. If it rains too much a week or two before ripe that's when you see the splitting and bland taste show up. Be happy your getting your deluge now vs. later!