It would be understood, but isn't the natural order for English. Putting "now" that early in the sentence suggest that suddenly, this very instant, it has become cold, whereas I think the German sentence just means that it is cold generally. If you were using some other adverbs such as "still" or "already", you could put them after the verb or after the adjective, depending on what sort of emphasis you wanted to convey
It makes sense to me, I think. Say you're standing outside on October 15 and the temperature is well below freezing. You could say "Normally it does not get very cold like this for a couple of months, but this year, it is already very cold." I don't think it translates this sentence well though.
You have a good point, but you're only aloud to say that because of the very specific context. Also, that might not be proper English.....(but idk about that)
EDIT: Well, now that I think about it, it might actually be correct. Guess it just sounds weird to me, but depending on context it is acceptable.
To answer many of the questions in the comments here at once:
You can rearrange the sentence to: "Jetzt ist es sehr kalt." without changing the meaning.
"Es ist sehr kalt, jetzt." on the other hand is not good German. You may encounter it in conversations as there are always people making a sentence and adding something afterwards. But you won't read it in books or something.
The word "jetzt" is just "now". It does not say anything about how cold it was before or how could it might be afterwards. There is no kind of valuation or comparision either. All sentences using something like "already", "still", ect. add information to that sentence which there isn't in the German counterpart.
The range of possible meanings of "jetzt" is very similar to the meanings of "now". You can say: "it is exactly 12 o'clock now." and mean 12:00 and zero seconds or 'just' 12:00. You can say: "It is May now." no matter if it is the 1st, the 3rd or the 22nd May and so on. It is always referring to a time span which you are currently in without telling you anything about what was before or what will be in the future.