I see that I'm replying too late but there's a chance that some people might read this message and that can be helpful if it could. So I guess that the best period to visit Neelum is March and April. First of all it is the spring season and it's neither too hot or too cold. Plus, more flowers, colors, and greenery.
And as it is told in A.E Housman's Loveliest of Trees, is Cherry Now that in Easter season (Spring obviously) the Cherry Trees are covered with all blossom which looks like as they are "hung with snow". And Neelum got a handful of Cherry Gardens.