Hey!
Children through the 2nd grade tend to be the age where most of their Pokemon experience relies on knowing the names of the Pokemon through the anime. As most of the children in this age group are not advanced readers, many just play the games in a scroll fashion, meaning they just press A and learn what attacks knock out the enemies fastest by memory rather than word recognition.
As such, they are most familiar with the wild, outdoorsy, personal aspect of Pokemon, rather than the impersonal, computerized video games. Also at that age, they are still in the age where imagination can take over for them. "Pretending" to be trainers would not be a problem here at all.
Also, I'm asking someone else to step in for me, as I'm starting to drift out of the Poke-loop; what are the three "starters" on the anime right now? Generally, when receiving their "Pokemon license" to be trainers, they choose between three Pokemon which they'd like to start with as their first; it used to be Bulbasaur, Charmander and Squirtle, but I don't think those good old days are aired on TV anymore.
Finally, I live in Rhode Island where we're quite accustomed to accomodating physical fitness and creativity into the program that function indoors due to inclement weather; our winters usually start around Halloween and last through April. If snow is an issue, I know plenty of cheap ways to build obstacle courses (for under $20, even!) and, geography permitting, you could even have supervised sledding with an "Ice-type Pokemon" theme. I can give details on that if you like.