It's funny, but the closest I ever came to being "Bit" in the woods was a similar situation - out for a day hike, with friends, in late may in the Catskills of NY - I was ready for rain/drizzle, but I was NOT ready for SNOW on the week before Memorial day in that part of NY

Started to show symptoms of hypothermia - I realized it, as did my companions - one loaned me his spare jacket, while we fired up the stove and cooked up some soup - while eating, the sun came out, and temps rose about 10 degs. I WAS ready to deal with 40 degs - it was that darned SNOW in late May

We finished the hike, simply because we were about 20 minutes from our turn around point anyway, and KNEW that even if it started to snow, I had enough gear WITH the stove and food to be fine - but it did teach me a lesson about how fast things can go bad