Go for it! This year I walked from Merida to Salamanca in March. Apparently I missed a few days of heavy rain just before I began (early March), which of course was good. During my walk there were some very muddy, wet spots because of the rain; once, I had to take my boots off and wade through the water, as it was too wide and deep to hop across. But no rain fell on me.
And yes, I hate hot weather too, so this was great. You didn't have to worry so much about water, because you drank less, and you were never too cold if you wore shorts or too hot if you wore pants.
Of course, prepare for some rain. But you can also get rain the fall, as I did during a previous Camino in November.
Oh, and re: pilgrims on the trail, I didn't happen to run into almost any -- maybe 5. However, from what various innkeepers told me, they'd been hosting a few pilgrims every night.
Have fun!
Melanie