No. Buying in the summer or spring would not result in a cheaper price. . That said, prices go up yearly due to increases in various costs.

+1 And many of those increases take place at the beginning of the year so they are happening now.

It depends upon the installer. I may drop prices if I am slow and need beer. Now is a good time to start pricing things out since it is typically slower.

As you may have seen on some other threads, this is the time of year where you might be more likely to find some crazy- low pricing. Not all companies do, but some will just to stay busy.
In regards to weather, it can be more difficult to schedule things in winter, but that probably depends on location.