Technically no it is never too cold to snow or too hot to rain. But there are times when the temperature of the atmosphere will limit the chances of seeing precipitation.

When the air is really cold (we're talking well below zero) the air is also extremely dry and this will limit the chance for getting snow simply because the moisture is lacking. But there is always some at least some amount of moisture in the air so really it can't ever be too cold to snow. Places that are bitterly cold in the Arctic still see snow.

With regards to heat, a similar principle holds true. When the air is hot (well into the 90s if not in the lower 100s) the air becomes very buoyant and will easily rise. Remember warm air rises and cool air sinks. For thunderstorms to develop we need the air in the mid levels of the atmosphere to be cooler than the warm air which is rising. You see the rising air parcel needs the surrounding air to be cooler to build into thunderstorms. If that rising air is warmer than its environment, it will keep rising and thunderstorms will likely form. But if the surrounding air is warmer, then the rising air will stop and no storms will fire.

We see this in the summer quite often when cumulus clouds billow up in the afternoon heat but don't get tall enough to produce any rainfall. We refer to this as a cap in the atmosphere. The warm layer of air aloft acts as a cap or lid on the atmoshpere, stopping any storms from forming.