Coaches telling parents that their 8 year olds need to do weight training and conditioning class.
And it is, not to put too fine a point on it, bull hockey.
Pre-pubescent children not only do not need weight training and strengthening, it's pointless because they don't have the hormones yet that make weight training in particular useful. They simply will not build muscle no matter how many push ups they do.
That said, you can, and should do stretch, strength, and aerobic activities with very young children. However, it doesn't have to be run by the skating coach, it doesn't have to happen at the rink, and it doesn't have to be boring.
The best strength equipment for little kids is monkey bars and climbing walls. Further more, it's a lot more fun than hand weights and push ups, which is the number one thing you need to do to engage young kids in "exercise." Playgrounds in general have everything you need-- equipment that encourages strength (monkey bars), coordination (various climbing apparatuses), cooperation (see saws), etc.
Here's your aerobics. If your Juvenile or lower skater is competitive, talk to your coach about making her "season" the non qualifying events in late fall to early spring so she can do field sports in the fall.
If she or he is already doing the qualifying events (which happen in the fall right on top of soccer), then you're switching your aerobic sport to spring. In-season, your little competitor should be running or doing other aerobic activity before getting onto the ice. Don't worry too much about things like Maximum Heart Rate for little kids, but if you're interested, here's a nice description of the issue that also deals with children and their specific needs.
Dance is great conditioning for kids-- it's fun, there are many reputable, vetted programs to choose from, and it covers strength, balance, muscle tone, conditioning and aerobics as well as great lessons in focus and discipline. Most skaters choose ballet, but for boys in general and for girls who balk at ballet, you can get the benefits of dance training from hip-hop, jazz, tap, or modern dance classes. (Older, competitive skaters should take ballet.)
Martial arts are another great multi-benefit activity for kids too young for dedicated weight or aerobic training. It offers all the benefits of dance, and is a good alternative for boys.
What do your younger skaters do for off- ice training?