Lumps are different from ruts. Even on a rigid bike lumps and bumps are pretty easy to navigate. You basically just ride up and over them. The problem with ruts like in your video is that you have to ride with them rather than over them. You, literally, get stuck in the rut and can't get out of it. You probably found that out on your ride. There are some ways to deal with ruts on a rigid bike but they aren't as effective nor as easy as using a suspended fork. The techniques are a whole lot easier to learn off-road as well because you have more chances to practice them.

That said, perhaps the best way to handle rut is to treat it like deep sand (again, something that you encounter more commonly off-road). To ride in snow (or sand) you want to try and float the front wheel over it. To do this, try to unload the front bars by leaning back more...almost as if you are trying to do a wheelie...and gripping the handlebar lightly. The rear wheel will dig into the snow or sand and you'll start to bog down but that can't really be avoided. The front wheel is going to bounce around a bit but that's what you want. Let the wheel find its way through the snow ruts as best it can.

To handle the rear wheel, shift down to a low gear and spin at a fairly fast rate. Do not mash! You don't have enough power to "power through" soft surfaces so you need to depend on "revving the engine"...i.e. you...more. Spinning at a fast rate takes a lot of energy so the longer the ride, the harder it will be.

This, by the way, is stuff you learn very quickly when mountain biking. You may never have to learn all this...and a whole lot more...on the road but it's beginner stuff for mountain bike riders. That's a really good reason to own and use a mountain bike. You live in an area that has excellent mountain biking in just about any direction you care to go...don't ignore the eastern part of our great state! If you have been looking for an excuse to own another bike or you just want to channel your inner kid, learning how to ride off-road is a great place to start. And it will make you a better rider all around. You'll quickly find yourself looking at your commute as another challenge, especially in the snow. You'll become "that guy" at work