Why is the east side cheaper? I mean, I know it was occupied by the Soviet Union back in the day, but why is it still cheaper there now?
Germany has a very low fertility rate & even immigration isn't enough to make the population grow more than very slowly so if a lot of people moved westwards and into the cities it means a lot of people moved out of the east and the country side.
Also almost the entire country is fairly flat & with a mild climate.
And Germany actually has among the highest amount of immigration in the world so not sure why you think they don't let people in. In my experience it is actually easier to move here than to the US (I'm an immigrant).
The places where it's a problem are those that people leave, like Bulgaria and Romania. There are basically enough "cheap" immigrants available from poorer European countries that the wealthy ones don't need to also additionally increase the rate of immigration from outside Europe.
All depends where you're coming from. w.r.t weather, I found winters in Toronto less depressing than Paris because Toronto at least had clear skies.