The best time you to catch trout are the days that end in "Y" and the months that have at least one vowel in them. I have caught them in the heat of the summer and I have caught them when I should've been out hunting the cooler weather. There's no wrong time for trout fishing.
The Red, Spring, and White rivers are good rivers to catch trout because the water temp is the same year round. Trout like cold rivers/streams/lakes. During the colder months, the water is actually warmer than the air temperature. Check the regulations, some areas only allow a single barbless hook as a lure. Some areas are catch and release only. And other areas might be closed seasonally for fishing.
Beware of generation, though. When the dams are generating, the water will rise and will make fishing difficult, especially if you are wade fishing. it's probably not as bad if fishing from a boat.
Good luck!