Yeah, like OR says, it is a fair uphill pull from Rincon Creek to Manning Camp and then a bit more of a climb to cross the range just east of Mica Mountain. There is a junction there with a spur trail that will take you to the summit of Mica Mt., the high point in the Rincons. From the junction, is is downhill to Italy Spring. I suspect that you will be hiking on, or around, snow from below Manning Camp to near Italy Spring. You will be hiking through some beautiful pine forests in this section of the trail though. Italy Spring is on a generally north-facing slope and can be snowy.
I don't like trekking poles either but got so accustomed to carrying an ice axe in one hand in the old days that I now carry a single, collapsible trekking pole and like it a lot. The thing I like is the sharp, grippy, carbide tip that holds well on ice and wet rock. I just collapse the pole and carry it on my pack if I don't need/want it. The one I have is made by Leki and has a handle like that of a cane; seems somehow appropriate for someone my age.
May I walk in beauty.