Mao's Red Army famous Long March took more than a year to
complete. The distance is between 6000km to 10000km depending on
who you believe.
http://www.taipeitimes.com/News/front/archives/2003/11/06/2003074739
Let's assume it is 6000km, and also bear in mind that it is an
entire army of many thousands, so it'll move slower than a small
compact force.
So is it possible for a smaller, very tough and very mobile troop
of ROK marines to complete 4000km in one winter?
I wouldn't say it is entirely out of the question, but very
unlikely.
After moving such a distance, many of the men will probably have to
retire from service in an elite unit as such a trek would do all
kinds of irreversible damage to the legs especially.
In Mao's case, many died during the trek.