To determine the wet or dry nature of the runway might be possible based on looking at aircraft stopping performance. Depending on how good your data is, of course, and depending on type - an autobrake type that targets decel rate wont tell you as much as an older type without autobrake I suspect.
If you have good data for the braking system you could perhaps look at a/skid behaviour.
I suspect you only have QAR/FDR type data, though, and it would be very difficult to use that for these purposes as the frequency is probably too low.
Why not do things the other way around - instead of trying to establish wet/dry for all data points, only use data points where you can be confident (to an acceptable level) of the runway conditions.
Check the weather reports for an airport where you have lots of data (one of the hubs, perhaps). Find a day where it didn't rain at all - dry for sure. Use all data that day as "dry". Find another day where it rained for a long time. Use data from that time period as wet. Bin the rest of the data.
If you see no strong difference in TR usage between the "known dry" and "likely wet" data that'll tell you what you want to know I think?
Indeed you could even compare the "known dry" data to all data - if the usage pattern differs between the dry subset and the rest, that implies the usage is different on non-dry days.