Whipping is done to lock (keep from pulling out), finish and protect a braid like the one pictured above. Without a braid/splice, you are relying on the whipping line to hold the eye. Might be OK for light loads, but I would not trust it to hold for pulling heavy logs. You can certainly try stitch-whipping an eye without splicing the eye in the rope itself, but I wouldn't expect too much from it.
I think this double braid eye splice might do the trick
. I haven't tried it myself, but it looks pretty straighforward to do, and has pics with the instructions.
There's also this PDF that addresses different splices: New England Ropes splicing guide