I do stake my two out occasionally; it's more of a factor if they are not too fat and can handle the extra calories. I did a few things to make sure it was as safe as possible, but as others have mentioned, it is never completely safe. Here's what I did:
I bought the screw-in type stakes for big dogs. These have a turning thingy at the top and it is nearly flush with the ground so it can go round and round without tangling.
I bought a very thick soft cotton lead rope off a spool at the farm supply store. I then had a snap attached to each end. I think I went with 15' in length.
I knew my horses. The two I stake are 12 and 16 years old. I've had them for many years and know they are sensible and just hold still when they are in trouble.
I stake them out where there is nothing for them to get stuck on, only grass. I don't put them close enough that they can tangle with each other either.
I don't leave mine out more than a couple of hours, but if you do, be sure to offer water during that time. I know that when I put mine back in the paddock, they head right for their water trough.
Lastly, I supervise them almost 100% of the time they are staked out. I take an iced tea, a good book and a comfortable lawn chair out to their general area and enjoy their company. Sometimes they come and say HI, but usually they are pretty preoccupied with enjoying such a nice treat as fresh grass.
My two go NUTS when they see me dragging out the stakes; it is such an exciting event for them! They will dance all over their paddock, but when I bring out the halters they hold stock still because they know if they don't behave and walk nicely, they get put right back.
Hope this helps! Jayne