Great Question!
I like this topic as it brings out a very important, but seldom discussed topic outside the recurrent classroom!
Please excuse me if I seem rather redundant here with this post, but it seems that there are conflicting messages out there with regards to V1 adjustments.
first off, I assume that everyone on here knows why and how you do Reduced power takoffs, and also with regards to reducing V1. When dealing with anything other than a dry runway, normal ops,(no performance affecting MEL's), you can never reduce to a flex or adjust V1. Wet or contaminated means that you apply full to pwr and fly the regular v speeds. there was a post that said that v1 is affected by thrust reversers, and this is not the case, when transport category aircraft are certified, ALL RUNWAY PERFORMANCE is certified WITHOUT the use of TR's. now there is sometimes a case when an airline sets itself apart and spends oodles of money to get a special certification beyond what is normal, so unless you were told and trained from initial that this applies to your specific airline and ops specs, then the normal transport certification protocol applies. there was another post where it talked about the 35' height and this stands for all aircraft and is rock solid and doesn't move. this is but the tip of the iceberg as the rest of TERPS must be followed as well which states: obstacle clearance is based on the aircraft climbing at least 200' per NM, crossin the end of the runway at least 35'ft and climbing to 400ft above airport elevation before turning(which is why your profiles have you turn after 400!) unless otherwise specified in the procedure. a slope of 152' per NM starting at 35' above the end of the runway is assessed for obstacles. a minimum of 48' ft per NM of obstacle clearance is provided in the assumed climb gradient. .......then it goes on to say that if obstacles penetrate that 152' slope then that is why you have a specified IFR departure procedure. Now there is more regarding what kind of climb gradient you must achieve single engine for 1st. 2nd 3rd segment until reaching 400' ft based on whether you are 2-eng or more, but we now get beyond the scope of the original question, but i just wrote this to set the record straight that TERPS procedures do not change and that is what all aircraft must meet at the minimum, so therefore changing your speeds or to pwr doesnt affect what you must minimally meet. there was another post that said that snow makes the to roll longer but in effect shortens the landing roll and that this somehow nullifies things!!!...huh? snow negatively affects both the to and landing #'s, and again the #'s dont care if you have TR's or a drag chute or anything....they are predicated on wheel brakes and speedbrakes alone! having said that, we know that snow now brings to life something called hydroplaning, so it makes the landing roll LONGER, not shorter. hell, just look at your tab data for any airplane, it will tell you the same thing! Now Mercury is right on with the wet vs contaminated data that comes from certification process! wet is demonstrated while cont is only interpolated. so again, V1 is affected by a multitude of factors(weight, temp, runway cond, MEL, to state some) when reducing it, you must take care to not reduce it beyond VMCA and it can never be more than V2(which only cares about weight). the older airplanes depend on the flight engineer for this tabulation while i guess newer airplanes may or may not do it for you, but in any case, unless you are normal ops, on a dry runway, To data is as published. I hope this has provided informative and If i am off base or dont make sense then i would be happy to elaborate more.
safe flying everyone!