Un-sprung weight (weight not managed by your suspension springs) will kill your MPGs faster than any other weight. A tire that weigh's more will have a dramatic effect on fuel economy as your engine has to keep that extra mass rotating at the cost of fuel. Worse is that it has to GET that extra mass rotating every time you get started from a stop, at the cost of fuel. The same applies to your brakes, which will wear faster due to the extra weight in your tires. Of course, AT tires will weigh more than "street" tires, due to the extra rubber in tread and the heavier construction.
"All Terrain" tires will wear faster on pavement, cost more in fuel, not corner or brake as well on asphalt, but will be much safer on gravel/dirt/mud and you could even add rain to that list (large grooves for water to channel out).
"All-season" tires are effectively poor at all seasons, but can generally handle the lighter side of both summer of winter. They will wear quickly in anything other than mild temps (no Arizona in July or Minnesota in January). They will perform blandly in wet and awful in snow greater than a small flurry.
"Summer" tires (aka high-performance tires) will have the best dry-weather grip of any tire, and only be OK in any rain more than a sprinkle. They will be completely useless in the snow.
"Winter" tires will have significantly more grip in temps below 40 degrees, and exponentially better the further the temps drop... but melt (and become very dangerous) in temps above 80 degrees (take them off as soon as overnight temps no longer go below freezing).
Hope that helps