Can dogs still get cold with all their fur?

Yes they do.
It doesn't matter how much fur they have on their bodies, although it does keep them warm' there is only a limit amount of time where their fur might just become covered up in snow and start to freeze up seeping through to their skin. Once that happens, they become cold and if left outside long enough on a cold winter's day or night, they might just freeze to death. It depends on how long they are outside for, though if it's not snowing or in a middle of a storm and just slightly chilly' then they should be fine.