Aye, the bosk do lay down, as do oxen, yaks, or other forms of cattle from Earth. (My parents have three VERY lazy Herfords, and those things are ALWAYS laying down!) I have always role-played leaving the bosk in the harness if the weather is poor and the ground soft from rain. If the weather is good and the ground is firm, I have thralls pound two study posts in the ground, perhaps twenty feet apart, and string a stout chain between the posts, to which I then tether the bosk by their nose rings with enough slack in the tether for them to lay down if they wish. I feed the bosk using nose bags filled with grain (then transferring the tether line to beneath the halter for the time being); I clip the small leather pouches to the ring on either sides of their halters. Buckets may be used if no nose bags are availble. To water the bosk, I fill a bucket time and again, carrying it to each bosk individually, that each may drink its fill before I move on. They can graze a bit of grass while in the traces or on the tether line.
And having once owned horses, I can say that it's not actually dangerous for them to lay down -- provided they can get back up again. Often one or two horses will "stand guard" in the field while the other(s) lay down to snooze -- a carry-over from herd behavior in the wild. But if you have an old horse, then it can be a very bad thing indeed for the horse to lay down. Its old legs may not get it back up again.
Good questions! ~warm smile~
