Personally I like my game cart, but that looked cool.
BUT - like you said, ticks could be a problem, and depending on the wound it could get real messy real quick.
I tried this many years ago (when I was young, strong and ambitious) with an average sized doe in Hocking county hills. No thanks. It isn't a new idea. Harder than it looks. I'll keep dragging short distances or going after the cart with wheels.
Pass!!! Maybe when I was 40 years younger. These days, I'll go get my Muddy Deer Cart and be happy.
I have a Jet Sled that works great, when it snows. Otherwise, it offers too much resistance, especially on mud surfaces.