I'm a physicist; you need a geologist or planetary scientist to really answer this. But from my very limited knowledge of planetary geology:

The minerals present on a planet depend a lot on what's going on inside the planet and how it formed. Planets with volcanic activity (e.g. Mars) will have igneous rocks whereas planets without probably won't; some minerals like olivine can be produced inside a planet but may chemically weather to other minerals depending on the atmosphere if there is any. But you find olivine on many planets and in meteorites, and it's the same mineral as the one you find on earth. Also some minerals need water to form - hydrated minerals found on mars can be indicators of past water in that area. Afaik the temperature (in the weather sense, not talking about volcanoes etc) in a region doesn't have much direct impact on minerals but can have a big impact on soils because it affects what life does, and that's the big uncertainty in your question about other planets. The "dirt" on earth is very different in a rainforest than in a desert largely because the rainforest dirt is full of living things and decaying organic matter, but the desert dirt is mostly mineral sand