Cold, hot, humid, dry...this will make exactly 0.0001% of a difference to your horns....in the short-term. If you are moving to a very humid climate (think, Florida), you may want to consider storing your trumpets in a relativity dry area. Eventually (after a long period of time), the leadpipe can start to wear (red-rot). However, these things are literally brass pipes. What could possibly happen?
Regular maintenance will nullify any climatic effects. However, playing is a different story. Cold & hot make a tremendous difference on intonation.