I broke mine two summers ago (screws and a plate, like yours) and I think I stayed out of the saddle for 6 weeks. It will take a while for the bones to heal, but the plate should stabilize and bridge the gap, so to speak. Perhaps your doctor is using the 3 month guideline to ensure as much healing as possible before you get back on, in case (god forbid) you should fall on that side again.
Never bothered me when I started riding again, but like you I think I did have some residual weakness and soreness that limited my lifting. I would say don’t try to rush lifting or doing too much hard work, but for me it was very easy to get back into riding and I never had a problem on the horse. At first I was a little tentative, as is natural after an accident, but it didn’t take long to get back to full speed. If your horse is a good egg and has been in work so he’s not too fresh, that should help too.
I had to wait about 3 days before I could get into surgery (and it would have been WEEKS if I’d had to wait to see a doctor out here; my sister is an orthopedic surgical assistant and her practice was able to get me right in), but as soon as the break was stabilized I felt a million times better. Everyone was amazed that I got right back into things after surgery, but I told them a little recovery soreness is NOTHING compared to how it felt before!
Obviously I’m not advising you go completely against your doc’s recommendation, but you might see if you can discuss with him why he suggested that time frame, what kind of benchmark he’s like to see for healing, and explain how you plan to minimize potential trauma.