To add some technical explanation to what larrybud said: Docker containers aren't full VMs. They don't virtualize the computer hardware or the OS kernel. So when you run a bunch of Docker containers on a computer, all of those containers are still using the same underlying OS kernel. Docker really only natively runs on Linux (and BSD), and all Docker containers are running in Linux, so running a Windows VM inside a Docker container would really only be possible if you also ran something like VirtualBox inside the Docker container (and I can't really imagine that working or being a good idea).

In short: VirtualBox is still probably the best option for running those IE VMs, and for cases like this Docker is not really a replacement for or competitor with solutions like VirtualBox.

Microsoft gave a big pile of cash to Docker to figure out how to make Windows based Docker images.

I haven't been following it closely so I don't know what's become of it since then, but if you want IE you're going to need that work.

For other browsers, the Selenium team maintains docker images containing all of the drivers and XVFB code to make them run. They even have a debug image with xvnc on it so you can spy on the browser if something is going wrong.

Not docker, but you can run IE VMs under vmware/virtualbox/hyperv by going to http://modern.ie and downloading time-limited IE images

Check out modern.ie, it should meet your needs