"Inclement weather" means unpleasant weather, which is stormy, rainy, or snowy weather. However, the phrase inclimate weather often is mistakenly used when the speaker really means "inclement" weather.
Amos: This is the coldest summer we have had on record. We need to do something about anthropogenic climate change.
Ignore Amos: Dude, there ain't no global warming! It's colder than usual this week, and don't you remember that inclimate weather we had this winter? That was cold, too!
Amos: Anthropogenic climate change does not mean just global warming. It also includes unseasonably cooler weather due to the melting of the polar ice caps. Furthermore, cold weather in the winter is not inclimate weather. I think "inclement weather" is what you meant to say.