Salty, Yes, that could be considered period correct.
BUT
Then the question would arise of correct for where and when.
If you are trying to emulate a Rocky Mountain fur trapper, the answer would be not no, but hell no.
If you are trying to emulate a Lewis and Clark exploration team member or maybe a Canadian voyageur, the answer would be no.
If your persona is an east coast farmer, the answer could be well, yes, maybe. Your story could be temporary lodging, just waiting to get your cabin built.
In short, if your person is involved in exploration or someone who was constantly on the move, it would be no. How the heck are you supposed to carry all that stuff.
If you are a military officer or the factor of a trading company, probably so. After all, you are a gentleman and who would expect a gentleman to sleep on the ground.
Or you could just be a modern enthusiast who is just plain getting too darn old to be sleeping on the ground.
The possibilities are endless. Pick one and don't apologize for it.
John