Is 1:00 AM a reasonable time for police to conduct a search of the room of a registered guest who happens to be on probation?Additionally they...

There are some unknown factors here that make a difference
in assessing whether police actions in this situation were either reasonable or legal. 
The first factor is why the police showed up at that particular hotel room at 1 AM?  It
is most likely they were responding to a complaint or a tip, either by the manager of
the hotel or someone renting another of the rooms there.  When they receive a complaint
specific to anything illegal in a location, a search is not unreasonable, nor would the
time be.

Depending on the state the incident took place in,
courts have often ruled that a hotel room is not the private property of the person
renting it, so the only consent they would need to obtain would be the manager's or the
owner's.  Lastly, it depends on the terms of your probation as to whether or not random
and unannounced searches of your property or person can take
place. 

Just based on what you have stated here, however,
you would have a difficult time proving police malfeasance.  Legally they are required
to identify themselves, but it is difficult to prove when they do not, particularly if
the person making the complaint has prior convictions.

From
West's Encyclopedia of Law:

readability="19">

Statutes may also identify conditions of
probation. These are actions that a probationer must do or refrain from doing during
probation. Though conditions may be spelled out in statutes, a sentencing judge retains
wide discretion to fashion conditions according to the best interests of both the public
and the defendant. In most states a probationer must not possess a firearm, commit
another offense, or possess illegal drugs during the probation period. Probationers must
also report regularly to a probation officer.

A judge may
place additional conditions on a probationer. For example, if a defendant pleads guilty
to assault, the court may order him to stay a specified distance away from the victim of
the assault. In a conviction for a small amount of marijuana a judge may order the
defendant to complete treatment for drug use. If a probationer violates any condition of
probation, the court may order additional conditions or impose a prison sentence that
does not exceed the maximum term of imprisonment that could have been imposed for the
crime.