Yes, most of the Eastern United States was forest, but No, tornadoes are not influenced by that.

Tornadoes are a result of meteorology and are not influenced by what is on the ground.

Even the smallest ones are too damned big to be effected by something as small as a skyscraper or a tree. They need weather pattern changing obstructions like mountains or the Great Lakes to even begin to alter their formation or path.

Most of the Earth's tornadoes occur mostly in North America, primarily in the portion of the United States called "Tornado Alley." Most of "Tornado Alley" is in the Great Plains region. This region has more trees now than it did prior to settlement by Americans and Canadians or many of the American Indians who moved onto the Great Plains after the re-introduction of the horse.

Tornado Alley gets so many tornadoes because of the unique meteorological conditions that exist there due to geography, specifically the collision of different pressure systems from the Gulf of Mexico and from the Canadian Arctic moving into the region at the same time and colliding. Usually this happens in from March to June, but can happen at any time.

Furthermore, while the Eastern United States, including regions in the Southeastern United States that get a lot of tornadoes, such as Alabama and Tennessee, were heavily forested prior to colonization they remain heavily forested now. And, when they were even more heavily forested, the land was cultivated by the American Indian in order to make it so, primarily using fire to clear land of underbrush. For more information, a guy with the last name of Stewart wrote a book dispelling the myth of the "Pristine American Wilderness" and the use of fire by American Indians to alter the North American landscape is now a commonly recognized fact.

Back to tornadoes, many people will point to the increased amount of damage tornadoes do now compared to the past and blame climate change. However, it is probably more likely that now more tornadoes are seen, recorded, and the damage they do is noted due to increased settlement in the region where they occur. I heard one meteorologist say something like, "Fifty years ago a tornado came through a pasture and the only way we knew was some trees were broken and some cows were missing. Maybe a house got destroyed or a family killed. But now that pasture is a neighborhood and dozens of families live where a few cows grazed. So the damage is a lot worse just because people are there."

The same is almost certainly true historically. Three hundred years ago, Tornado Alley was barely populated by a few nomadic hunting tribes and herds of bison. An F5 couldn't do much damage if it wanted to because there was nothing to damage and no one to write down what happened. Now, millions live there so the damage is much more noticeable.