yup, do the same thing. most of the time for me is the psychological of "crap! it's cold. do i really want to do this? why am i doing this again?" sort of thing. i remembered when i live in Minnesota, folks would go into the sauna for awhile, then got out and jumped directly into a pile of snow in the winter. i wasn't that crazy so i never did. i went to an aikido seminar one time and we stayed at a hotel that has the jacuzzi next to the pool. so i alternated between the jacuzzi and the pool, and my body didn't ache as much during the whole seminar. methink, going from hot to cold sort of trigger the anti-inflamatory process inside the body similar to ice your joins or injury to keep the swelling down. don't know how much of the icing the body, misogi, stand in the cold fall water, wading in to cold river, and so on would contribute to internal training. it could very well be external training like the muay thai fighters who pounded their legs and body on regular basis to toughen their body. or misogi through heavy consumption of spirits.
I spend a lot of time in Finland, where we go from boiling hot sauna to jumping in the snow (Or breaking the ice and jumping into the nearest lake!) I would say that if you find the cold part worrisome, your sauna isn't hot enough. We usually have it cranked up to around 100C, the first round is a bit shocking, but after that it really feels amazing. But I have noticed people doing the sauna at a much lower temperature and keeping the cold part the same, which isn't going to be nearly as pleasant. If you get a chance try it with a properly hot sauna, and when you get to the cold part, it is going to feel so wonderful you won't think about it being too cold.