I don't think that's harsh. I don't hold any children outside (unless they are hurt and I'm comforting them). I am not an outdoor winter loving person but we still go out when we can. This year I was lucky, there was minimal crying outside (the handful of times we did actually get to go out) but last year I had children who didn't like snow. The kids who like it play, I stand and watch and the crying kids stand/sit and cry LOL. I'm sure the neighbours love me!!There were a few times last year that I brought out the wagon and they were allowed to sit in there because I do think that 20-45 minutes of sitting on the snow would get too cold.
PS. I am so jealous that you have puddles already!! My backyard is still a mountain of snow with a round spot of grass from where I kept it shoveled for the kids to play