My experience with doing this many times causes me to offer the warning that the nosewheel lower attaching forging, and it's attachment to the firewall and belly skin are a little delicate. In particular in the fore and aft direction. It is also possible to damage the steering by turning too far.
Don't pull too hard on the tail tiedown ring either. It's intended maximum load is in the 700 pound range (down, not back), and bending of the bulkhead and doubler has been known to occur.
The original drawn aluminim tube hand towbar, and a fair amount of muscle are the safest way to move the plane. The towbar was designed to break before any airplane did. Other towbars and tugs may not offer this protection. I'm not saying that they won't work well and safely, but I pull my Cessna by hand.
If a Cessna is really stuck - a suitable rope or tow strap around both main landing gear legs (but NOT the brake lines or fairings) and the plane can be safely towed by machine, with a second person steering with the hand towbar.
Pilot DAR