Well, there are a few caveats.
For one, not all performance data is predicated upon ASDR=TODR i.e. a balanced field. It may not be possible for some types, for one thing (if you are limited by the single engined "go" case, then reducing V1 obviously won't help, and if V1=VR it can't go higher either ...)
Secondly, not everyone wants a balanced field calc - if you want to exploit a difference between ADSA and TODA, say, then unbalancing may be the way to go.
But, to answer the questions:
Does the TODR change when the runway is wet?
yes, though not much - there's a potential for some additional drag on a wet (though more on contam) so you may need SLIGHTLY more runway for the accel phases. It's pretty small, of course.
Does the ASDR change when the runway is wet?
Hell, YES. The "S" part of ASDR is a damned sight harder on a wet runway. It's the increase in ASDR (especially relative to TODR) which makes reducing V1 a good idea most of the time; reduced V1 reduces ASDR and increases TODR, bringing both back into relative equilibrium.