Does your compact tractor have front loader,if so back drag w/bucket somewhat level than use roller...harder ground less effected roller..no front loader wait until ground almost dry than travel outside of ruts mostly w/rear tires....and hand the young riders rakes.

 

I would say wet for rolling, and dry for bucket work, and as Thomas mentioned rakes for the boys cause you dont want them to miss all that fun..

 

I have both an areator and a roller - usually before a heavy rain ill areate so the water will help the grass better- i bot a poly roller when i had some tree work done and the trucks left ruts in the yard- id wait till it had rained heavy then get out and see if the yard would smooth out.

As far as i know, in the fall and spring are the times to roll the yards.