Safety and ease of towing are affected by the towing environment.

Traction is probably the most important component of towing. A great deal of power is lost as the tire breaks free and spins. Slick or dirty surfaces reduce traction. As with most wheeled vehicles, the best surface is solid, clean and dry.
Epoxy-painted surfaces are generally fine as long as they are clean. Dust and other contaminants can make this type of surface very slippery.
Should the tug tires develop a hard skin on the tread (glazing), wipe the tire treads with a cloth towel wetted with acetone. This will soften the tires and restore traction.

Gravel or dirt is never recommended. If you have these type of towing surfaces, consider grass pavers. These provide a better surface while still allowing a grassy look.

Inclines of over 2-3% can be problematic (highways often include runaway truck turnouts at 5%). Short inclines, such as shallow drainage ditches in front of hangars, are fairly easy to overcome, but may require a little practice.
Moving up an incline increases the effective weight of the aircraft.
Pushing down an incline can be hazardous as tug traction is reduced. Proceed slowly and with caution to help prevent runaway planes.
Going sideways across an incline can be tricky as the plane adds pressure in the downhill direction. This pressure can put extra pressure on gear hook-ups or cause carriage rotation on Lazy-Susan equipped tugs.

Thresholds, door tracks or rough surfaces can make moving more difficult.
Obstructions act like chocks. An obstruction of 1" or more should be addressed with filler or a small ramp as needed.

Snow and ice cause problems for most vehicles, including tugs. Consider keeping traction-enhancers like sand on-hand. If you will use your tug often in wintery conditions, invest in tire chains.