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Say a contract has a condition based on NOW being after a time. Is NOW UTC, and is this validated by each node before being added to the chain? Let's say you want ensure a function is called during a 1 hour window, will this be possible to enforce?

For example:

current stack state: NOW - 15 minutes :: NOW + 45 minutes //pseudocode
code: NOW; SUB; GT; SWAP;
 NOW; SWAP; SUB;
 AND;
 IF send transaction... FAIL; ;

This should check that it's greater than NOW - 15 minutes and less than NOW + 45 minutes, which are both true so it can execute the transaction.

It might also be important to understand how the network gets consensus on a block time across the network?

There is an assumption that all Tezos nodes are synchronized, otherwise the consensus with 1-minute slots would not work. Of course, some delay is ok, but more than a few seconds might prevent a baker from baking.

NOW is the time at which the block, containing the transaction, should be baked. So, the baker knows the last block time, he knows his slot, so he can compute the time at which he should bake the block. It then uses that time to execute the transactions.

Nodes time being synchronized is only part of the picture: bakers can always be offline for their own reasons, the network can be stalled, many other transactions could be competing to get selected by bakers, etc. so people need to be very cautious and give plenty of time for an event to occur.

I would say that a few minutes or even hours is not enough today.
Is one day enough ? I would tend to think so but I'm not even certain.

The baker chooses the value of NOW. I am aware of these two constraints:

The protocol enforces that the timestamp is at least the minimal timestamp at which the baker was supposed to bake (some delay after the previous block's timestamp): baking.ml.

The shell will also ignore a block whose timestamp is too far in the future (more than 15s) relative to the system clock: distributed_db.ml.