Wheels are a fascinating subject, especially for something that seems so simple. I have done some reading about them for different applications and have some experience making different hand carts (which really let you know what is easy and hard to pull) and some animal pulled items as well (though I often use skids for animals). The rolling resistance of wide tires is substantially higher than narrow tires, and the rolling resistance of low pressure tires is substantially higher than tires with high pressure. That is, as Donn correctly points out, as long as the tires maintain floatation in the terraign (think of narrow/high pressure tires on pavement or sand vs wide low pressure tires on pavement or sand). Overall, it seems the best efficiency is would be with tires that are as narrow as is required to maintain floation on the surface. If you don’t maintain floation, all bets are off as rolling resistance increases and efficency takes a nosedive. Rolling resistance for steel or other inflexible wheels goes down dramatically as wheel diameter increases. This makes intuitive sense to me, as the contact patch grows with wheel diameter and allows one to use a narrow wheel without having to sacrifice contact area and floation. You can see this in some historical designs as well, with tall wheels being very common for things like high wheel log carriers, ox carts, and wagon wheels (esp rear wagon wheels that carry more load). Notice these are not pneumatic tires. For pneumatic tires the situation is more complex because the tire surface itself compresses to accomodate the terraign which lowers rolling resistance and increases floation. Because of this multifactorial accomidation, pneumatic wheels reach a point of diminishing returns when is comes to rolling resistance vs. wheel diameter at about 30 inches or so. Today, most pneumatic wheels that are designed to make the most of limited power are in this range (bicycles wheels, fuel efficient cars, most logging arches). If you are substantially below this wheel diameter, there are gains to be had here, but if you are already using “car or pickup sized” tires, there is little more that can be gained using larger diameters.
Although I think this conversation about wheels is fascinating, I think the biggest source of drag in this system is going to be the dragging end of the log. If I had a winch, I would probably hitch up a tilt bed trailer behind that cart, winch the log(s) up onto the trailer to transport them, and then roll them off the side when you got where you are going. Having the load completely on wheels (IE nothing dragging) is going to give you a massive increase in efficiency. It could easily double the load you can pull on the flat. I predict the effect of the tires (given the set up you already have) will be subtle.
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