Unless you are visiting a love one, the rainy season is not only wet but the fog comes in adding to the extreme gray surroundings. From late december through March unless you can reach the sky with a paint brush to add some color, I would not ask you to visit.
Two things to watch out for in Upper Bidwell Park.
First, even during the winter the sun can be extreme. So apply sunscreen continuously. We were out on the trail for less than two hours and we could readily feel the effects of the sun in a short time.
As you get into the upper reaches of Bidwell Park the terrain changes noticeably. There are many wooded areas with stands of poison oak. Be careful, in some cases it is everywhere.
Finally, bring plenty of water. We saw no areas for fresh water when we were hiking. Whether it is a water bottle or canteen be sure to pack well before setting out on some of the hikes.
Chico can be very hot in the summer (as much as 110F sometimes), but it's a dry heat. You won't feel it as much as you would if there was much humidity.
It can also be quite chilly in the winter (in the 30sF, especially at night).
So, just a little waring to plan accordingly.