Storing things (for pickup later) or shipping them home will not be cheap. Whether or not it's worth it to you is subjective.
If you have (or get) small, light-weight (but still effective) rain gear, and an extra (thin but warm) later or two, it won't add much weight or bulk. And you know, it does rain occasionally in hot places, so you might actually need that extra stuff, even in hot places.
I have made trips that combine very hot tropical places (South Pacific islands) with the mountains of Japan in February on the same trip (I spent a week scuba diving in Palau, then went skiing in Japan). It did making choosing and packing things a bit more complicated than usual, but it can be done (although I'm sure some people in Palau wondered why we had thick winter gloves, ski hats and thermal underwear with us when it was 90+ degrees outside). Admittedly, we did leave our scuba diving gear in Tokyo when we went skiing... The point is, you pick your clothes for the hot weather first (and be minimal and choosey). Then add just enough extra layers and specialty items (rain gear) for the northern segment. It can be done!
