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As long as the plane is equipped for icing, which all airlines are, there is not really any added danger to flying in snow. Braking on landing may be affected if there's any accumulation but they keep close track on braking ability as each plane lands at the airport. Snow won't affect the way the plane flies as long as the wings are clear of snow on takeoff.
Actually, there are. Tracor Aerospace (now part of BAE) has a contract to turn them into target drones (called QF-4's), so the numbers are dwindling. The US military officially announce the decommissioning of the F4's (although actually doing so is still a work in progress, and some may still be serviceable). But the rest are unmanned drones.
There are some foreign countries still flying them, as far as I know. Parts are getting hard to find (especially engine "hot section" parts). Unfortunately, the US deliberately destroys those parts, so they cannot be used to keep other planes flying. Some of those planes still find a home, however, as "gate guards" it airports around the country.
Getting your aircraft pilot's license takes work (and money), but it is well within the reach of anyone of normal intelligence and physical ability. I've known college students who basically collected pop bottles for the deposit, and picked up part time work on weekends, and managed to get an hour or two of training every month or so. Took them a couple of years to get their license, but they managed it.
For a normal category license, you are looking at about 40 to 60 hours of flight training (actual time in the plane). Not all of that requires an instructor. Once you "solo," you will be allowed to fly by yourself (with the instructor's approval). Often the training aircraft will be older and very basic planes - but that's just fine. It's the basics that you are learning.
It takes lots of practice, and there is a lot of book learning (weather, regulations, principles of flight) as well. But you can do it if you want to. Most things that are really valuable take work.
Your question is a good one - but the answer is much more complicated that you would expect. Think about driving your car from point A to point B across a city. Lots of paths - some shorter than others, but the shortest path may not be the quickest. Or the quickest may involve a toll road - and you may or may not be in a hurry.
The usual most important factor (for commercial operations, at least) is to save money, while still arriving on time. Airplanes in the air are subject to the winds aloft, which will generally be at different strengths AND DIRECTIONS at different altitudes. Most airplanes operate more efficiently at higher altitudes (up to limits), but at those higher altitudes the plane may face stiffer headwind. Further, it costs time and fuel to climb to those altitudes, and you will not regain coming down as much as it took going up. [Think of a bicycle on hilly terrain vs. level ground.]
So what's the answer? Well, for most trips the pilot will consider all these factors. They are taught during training how to plan the flight in terms of time and fuel required, and to include in that especially the winds at different altitudes. Then they will pick the altitude, whatever that is, that maximizes the results that they consider most important.
Departure controllers have blocks of airspace with altitude limits. Chances are that there was other traffic that they needed to have out of the way so they held him at 5000 before clearing him to the next controller's airspace.