the snow is likely all melted in the area of Medicine lake this time of year(in winter you likely couldn't get there without a snowmobile or helicopter

I took a group of people out there in winter and almost got stuck in my Tundra 4 wheel drive but luckily I was able to back quickly and snap the wheel to turn us around quickly before we got stuck. So, we were okay. So, now in August is likely the best time to go because it is all covered with snow up there often for 6 or more months a year or more in this area. You can easily be 50 miles from the nearest person out there and often there is no cell reception at all so be sure to take Forest Service physical paper maps with you so you don't get lost also even in August. I have driven 25 to 50 miles on roads out there without seeing a single car so you don't want to get lost or break down out there so take water and food and maybe sleeping bags and a tent for emergencies even this time of year

Google maps says it is about 61 miles or 1 hour and 24 minutes to get there. Just remember this is very remote and so you need a full tank of gas to likely be sure you get into this area and back out as well as like I said before Forest Service physical paper maps so you don't get lost out there without Cell reception.