There are plenty such models with some in every category.

The highest resistance to inclement weather are waterproof cameras which are all point-and-shoot model with a sealed non-extending lenses. These can even go underwater between 3 to 12m for a minimum of 60 minutes.

Weather-poof cameras are sealed against splashes in any direction but are not protected against water pressure. For an interchangeable lens camera, a weather-sealed lens must be used to make the whole thing weather-sealed. In some limited cases you need to add a filter to the lens to complete the seal.

Weather-proof lenses are available for various mounts but some like Sony Alpha and Micro Four-Thirds mounts have an extremely limited number of weather-proof lenses. There are none for the Fuji X mount. Olympus makes a weather-sealed Four-Thirds to Micro Four-Thirds adapter so you can use weather-sealed Four-Thirds lenses on Micro Four-Thirds cameras.

There are several cameras and a handfull of DSLRs - all from Pentax - which are also freezeproof which makes them suitable for extended usage at sub-zero temperatures. Living in Canada and having owned all such DSLRs, I can attest to this. I have also taken my K-7 and K-5 in heavy rains and in several desert sand-storms and have had no trouble rinsing them (with lens attached) under the tap to clean them after. Needless to say, I am not worried about rain :) Incidentally, Pentax also makes the cheapest weather-sealed DSLRs and cheapest weather-sealed lenses.