Is it safe to condense water into a liquid nitrogen trap?
One use of a liquid nitrogen cold trap is to collect organic and water vapors that are removed from a system under vacuum.  In this case, the vapors are collected as ices (solids).  See this reference which has some useful information on Schlenk line safety and use.

Where you want to be cautious is when your collection is finished.  You do not want to keep a liquid nitrogen cold trap exposed to the atmosphere because oxygen will condense and cause an explosion hazard.  Typical procedures would include shutting of the vacuum pump, dismantling of the vacuum apparatus and allowing the trap to warm to room temperature (in a fume hood if organic vapors were collected).

Some additional references might be helpful, including this one that not only describes proper Schlenk line technique but also provides some good references; and you can see how liquid nitrogen traps are used for several industrial purposes here and here.