In my opinion, the best way to take out trees is with an excavator. If that's not an option, then a backhoe, which is what I have. For small trees like you described, most of the time I can just push them over by putting the bottom of the hoe bucket against the base of the tree and working my way up, while pushing it over. If that doesn't work, then a little digging on either side and they come right out. For smaller saplings I use the teeth of the bucket to push the tree over and pin it to the ground, then I move the bucket sideways a few inches an pull the bucket back towards me. This creates a hook in the tree where it's bending and I can quickly pull it out of the ground. I did this with hundreds of trees over the last weekend while clearing an area for a new fence.
I would not use a dozer. I own a pretty good sized dozer that's 40,000 pounds and 170hp. It pushes most trees over alright, except when the tree snaps off and leaves a stump. Then that's a big mess. The big problem with a dozer is getting the trees to where you want to burn them. Even with a rake you will end up with tons of dirt in your burn pile.
My neighbor has had a lot of his land mulched. The day its done, it's really nice. But nothing grows there for awhile and you cannot plant anything in all of the chips until they rot away. In six months it's all weeds. A year later it looks worse then before it was mulched!!! You really have to spend a lot of time working the ground after it's done to have nice results. In my opinion, it's a lot of extra effort to accomplish this.
Getting the trees out is the easy part. Getting them to the burn pile is where you will spend all of your time and energy. Dragging them creates ruts and it's very VERY SLOW. A grapple is by far your best friend. Nothing is faster, cleaner or easier then picking them up and carrying them to the pile. I modified my backhoe front bucket to be a Quick Attach so I could remove the bucket and put on the grapple. Now I can remove the trees with the hoe, and then turn around and use the grapple to clean up my mess. A quarter of my time over the weekend was removing the trees, the other 75 percent of the time was picking them up and hauling them to the burn pile.