I have fished as late in the season as January some years, where the line-guides would freeze from the water coming in on the line, but never had a problem with the poles integrity.
I have also fished as early as Ice-out many years, where ice was still on many parts of the lakes or ponds, and again, no problems. I got Bass Pro Shop's rods...
If the particular rod has a composite reel seat and the reel is tightened to the rod, the reel seat can crack in the cold weather. Simply loosen the reel a bit between uses. On the other hand, if the reel is held in with metal rings on both ends, you are OK.