I spend time almost every weekend in the canyons (mostly Provo Canyon, but mix in other canyons regularly) hiking, skiing, snow shoeing, paddle boarding... year round, all seasons, most any weather condition.
Hiking Timp. for the most part is not enjoyable. A not insignificant part of the hike is through ugly terrain and across unstable terrain. The view from the top is awesome. I probably won't do it again. I wouldn't really recommend it to anyone that isn't really into hiking, very young and/ or quite fit. Was never on my bucket list. Did it with my son and a scout group. Overall much of it was a meh experience. I literally live 3 miles from the mouth of Provo Canyon and have for nearly 30 years.
My late next door neighbor climbed Timp. annually into his 80s. Not my thing. Plenty of other beautiful places to visit and plenty of other wonderful activities to prioritize.