Holy Smoke! That IS a lot of smoke! Sorry, I couldn't resist. Yes indeed, a pleated-type paper air filter element that is loaded to the max with dirt and debris will cause that. Some diesel engine systems have a warning indicator that the air filter needs cleaning/replacing, which operates by monitoring the engine air intake manifold pressure, or rather lack thereof. My Caterpillar D4D crawler has such a device on the dashboard, which is actually a very simple type of vacuum gauge.
With the air cleaner maxed out full of dirt, the outside of the radiator core very likely needs cleaning to get shredded grass and weeds out of it, too. Blow it out with an air hose or use a spray nozzle on a garden hose to wash all the stuff out, clean it from the side the engine fan is on from under the hood. Be careful not to get any water into the air cleaner intake. And NEVER get water anywhere near the air cleaner when the engine is running! If the engine sucks water into it, it will be destroyed!
Since you say you are new to tractors, as well as that you were unfamiliar with what could cause so much smoke - - - for your future benefit as an owner of one of the best wheel-type tractors made (in my opinion based on owning Kubotas since 1981), find and read several books on simplified four-stroke cycle automotive-type diesel engines (as opposed to humongous marine engines used in ships and municipal power generation). Don't get any books with diesel engine sections more than maybe 20 pages. Also get a few simplified books on modern wheel tractors with three point hitches, and one more simple book that covers the basics of hydraulic systems including hydraulic cylinders. You don't have to sit down and read all this stuff in one week or month or even one year. The idea is so you have some idea of what's going on with your tractor, and have some kind of reference books handy where you can look stuff up. I've been at this business since 1968, and diesels since 1971. For me, it helped a lot that I really like working with these machines, along with the industries where they are used, as well as maintaining and repairing them. Just remember that these machines can hurt you, that is a big reason why you should read some stuff about them so you understand how they work. I'm not a big fan of youtube videos, there is a lot bad stuff out there that will trip you up when you know nothing about the subject. For this reason, I prefer good old-fashioned books. Good Luck!