It is easy to burn things in the dry season, not so much where it is wet. Eastern North America generally qualifies as wet, certainly in the winter, less so in the summer. This isn't to say that you CAN'T do slash and burn where it is wet, since it is done in rainy Papua New Guinea an the Amazon, but it makes more sense as a strategy when there is a clear rainy and dry season. A forest or scrubland area will be cut in the wet season, allowed to dry in the dry season, and then burned, returning valuable nutrients to the soil. The soil can then be farmed for several years without needing further nutrients. The burning during dry is key, because it allows the burning to be done between two growing seasons (the wet season). In Eastern North America, if you tried to burning during the dry season (summer), you would lose that growing season, and have to find another source of food that year.
The other side to the dry season is the wet season. Seasonal climates will almost all see much more rain in at least one month than anywhere in the eastern US, which has remarkably stable precipitation all year. Therefore, the washing of nutrients out of the soil happens more quickly in the tropics.
Many places where slash and burn agriculture are prevalent had poor soil quality. Tropical environments tend to have more leached soils due to heavy seasonal rains (or heavy year-round rains). That means that burning is an effective way to add soil nutrients. Areas brought under cultivation from forest-land in Northern Europe have remained productive under cultivation for at least 2000 years (in the case of northern France and England) due to the fertile soil layer. I suspect Eastern American soils have similar vitality.
The rainforest, on the other hand, retains almost no minerals and can be exhausted quickly. The only way to effectively farm is to cut down and burn the minerals in the living plants and trees to return them to the soil.
This is a little more theory than fact, but in the tropics, there are many leguminous trees, while in the northern latitudes there are many leguminous ground plants. African savannah-forests are dominated by acacia, mopane, and miombo. These are all leguminous trees that add nitrogen to the soil. No comparable array of dominant tree species are available in the northern latitudes. In America and Europe, soil fertility was traditionally restored with vetch, clover, alfalfa, or (nowadays) soybeans. Those are single season plants; in the case of clover and vetch the can be grown as a meadow in a year or two of fallow. The trees in the tropics, on the other hand, need a longer time to establish. Therefore, it makes relatively more sense to do a yearly fallow rotation in the northern latitudes, and a slash and burn many-year rotation in the tropics.