The ankles and muscles foot to knee are particularly challenged. Similar question to this here on marathons but now focus on skiing and external weights can be used: this can be related to roller skiing, ice skating and skateboarding where the legs, pelvis and core strength are demanded. So
What are some good strength exercises for different skiing practises?
Lunges and balance are good ideas but I would particularly consider exercises that focus on core and legs. Burpees and updowns are particularly good because they improve leg explosion and engage the core pretty heavily while also working on smaller muscles that increase balance. Burpees will also help with shoulders to accelerate as a racer out of the gate.
If you want to include weights deadlifts are also helpful in that they engage the back as well as the core. Really all the classic leg lifts will help. I've also seen a lot of ski workouts that include weight sleds or drag shoots.
One big thing to consider would be any exercise that engages your core by throwing off your balance. Bosu exercises come to mind because you constantly have to be maintaining your balance. Bosu stepovers would be particularly good in this case.
Have you seen people running marathons and they need to run it backwards halfway because of too much pain in knees?
This is because of overdoing forward motion. Ortopedists and physiotherapists often find such customers and interestingly this is related to strength exercises for skiing: when people overdo going forward, they forget the other motion that is going backwards. Skiing requires balance between backwards and forwards particularly in lower legs. Going only forward can compromise your balance so integrating both directions to training is healthy way to improve the strength for skiing because the strength must be balanced.
One of the easiest way to work the "ankles and muscles foot to knee" is to go backward: backward running works the muscles such as calves, shins and front thighs. Going backwards also improves the balance in lower legs. More benefits. Then combine this with things such as Backward skating, Backward slalom skinng like here and have some fun.
You need to find balance in many levels such as muscular level, neural level and coordination. It is a bit like frontstroke and backstroke in swimming.
