In the new Total War game there is a feature where the winters get increasingly cold as time goes on, is there any evidence that this happened in real life?

to clarify this is Total War Atilla and goes from 395 to time x (couldn't find). While the idea that there is a constant trend of winters getting colder throughout history is wrong there are climate periods of increasing warmth or coldness. There was a "Roman warm period" from 250 BC to 400 AD and as that implies the next years were colder.