I don’t bother with changing tyres. Always 2.5″ High Rollers, ST on the front, 60a on the back.
Having said that, both my bikes are dressed for the same purpose and I don’t race competitively or worry about how long a climb takes. If I was serious about racing – XC or DH – then I would absolutely change tyres to suit the course / weather.
As it is, the most important thing to me is grip on the way down, so I stick with tyres that work for that and compromise on the ups.