I've done Florence Peak as a winter snowshoe hike/ scramble, though years ago. That route very nearly follows the one your map shows. Although you are indeed "never completely safe" from avalanches, I don't recall much hazardous terrain, and going to the lake should be reasonable except under very unstable conditions. Driving to the TH is arguably as risky. If you have enough daylight, clear skies, and stable snow, mosey on over to the top of Florence to satisfy the peakbagger that lurks within and get a fairly good view of the N side of Rainier.