If a human driver is unable to drive in certain snowy conditions, then we shouldn't expect a level 5 car to.
Problem is that level 5 doesn't state what kind of driver should be the standard. A 70 year old would likely crash more than a 20 year old in snowy conditions for example.
With that said, I don't think a Tesla would do all the things a Level 5 has formally stated to do. For example, a human is able to drive a car inside a mall (perhaps to park a car for a give away sweepstakes). Tesla hasn't trained their software to handle that capability but a Level 5 formally says it should be able to carry out that task.
Yes, true level 5 is very, very, very, very difficult. We have had a pretty snowy winter. I need to do parallel parking in relatively tight spaces with knee-deep of slushly snow (with progressively hardening bits of ice in it). Having more than two decades of that experience, I only get stuck a few times a winter. That is why I have a snow shovel in the trunk, as do almost anyone else who needs to park in the same snowy mess before someone cares to come and collect the snow. (And once it comes, the cars are behind a hip-deep wall of snow. Shovelling is great exercise, but slightly beyond autonomous vehicles' capabilities.)
Another wintery example. When the friction coefficient is low, it is often different for different vehicles depending on the tyres and ABS/ESC functioning. So, an autonomous vehicle must keep a long distance to play safe, as it may happen that the vehicle in front may have much better grip. However, if all cars keep — say — a three-second distance to the car in front of them, the road capacity is less than 1200 vehicles/lane/hour (as every vehicle takes more than 3 seconds). Still, in practice there are at least 2000 vehicles per lane per hour. This, of course, means that if something unexpected happens, local garages will be employed for a while.
But we accept the risk, because otherwise the traffic would come at a standstill. Our traffic system is built that way. (The friction coefficient is important here, because inter-vehicle communication does not help much with this specific scenario. In dry conditions decent V2V helps to reduce distances.)
I know snow is not a real problem in most parts of the world, so it is an extreme example. However, level 5 definition carries the words "in all conditions". Of course, "the most skilled driver" and "all drivers" are different, but even when we talk about the median driver, the problem is there. Removing the steering wheel from the car is difficult unless we accept autonomous vehicles may take relatively large risks — just as human beings do. I do not think we will. We need to rethink vehicle traffic — both the road environment and the legislation – before level 5 happens. It will take decades.
Level 4 is more realistic, because the definition is that the car drives by itself in limited conditions (limited weather conditions, limited geographic area). That may happen relatively soon, but it will be restricted to good conditions and certain roads. Highways are the easiest environment, but local taxis/deliveries in some areas may be possible within a few years.
(A reality check. We are right now at level 3; the driver needs to be ready to take control, and the cars are at level 3 only in good weather, on certain highways at below 38 mph.)