The post office will forward the mail. But, if the letter says " do not forward" or words to that effect, it will not be forwarded.
The first year we snowbirded, we missed some bills from a doctor, because of that.
Also, we had trouble getting some annual enrollment papers from the insurance companies.
We try to do all of that online now, but some places just aren't online yet.
Now we rent a po box, and use the premium forwarding from the post office. This gives us all our mail. It is pricy, though.