What do you think the answer is?

Paralysed is fine if you mean the snow has brought everything to a standstill. If it has just delayed everything, then any of the other words are fine, although I agree with Robert, it sounds like a news report, not everyday conversation. "Transportation' would means all means of transport - road traffic, trains, ferries, planes. If you just mean vehicles on the road then 'traffic' is generally used.

They are all possible, depending on how you view the situation. (by the way transportation should not have "the") paralyzed - nothing is moving impeded, hampered, hindered - for these, transportation is moving but with more difficulty than normal I do not know the context, but this is not a local traffic report. The wording is more like a news story about elsewhere.

If the point is to say that the traffic is still moving but slowly its impeding traffic, thou hi hindering can also be a viable option