I got a free lesson with a personal trainer at this gym I used to be a member of and I had him give me a workout routine that would help get me in shape for snowboarding season and it has done wonders for me getting ready for the season.
I use an indo board and do 3 sets of 15 squats while balancing on the indo board with 15lb weights in each hand. Not only does that stregthen by legs, but it helps a lot with my balance and working the smaller muscles and core.
You can also squat against a wall with your legs at right angles and stay in that position for several minutes at a time and do a few sets of that, that will help your legs gain endurance for being in your snowboard stance all day. (note: if you're not bending your knees through your turns then you're doing it wrong) You can start with three sets, 1 minute long each and increase your time from there
Then I do one legged squats where you stand, for example, with your right leg on a step or ledge about 8-14" higher while the left leg hangs over the edge. You have 10-15lb weights in both hands and you squat down with the right leg until your left heel touches the ground below and then raise back up. 3 sets of 10-15 reps each leg
Next I do calf raises with my heels hanging off the ledge with weights in my hands doing one calf at a time or both together. 3 sets of 15-20 reps each leg.
Pushups help with your upper body strength including your core too. Just think about the number of times you push yourself up from the kneeling or sitting position throughout the day while snowboarding. 3 sets of 6-8 to start and then build up from there.
To strengthen my core, the personal trainer showed me a bunch of different plank exercises to strengthen my core that killed me, but ultimatley strengthened me way more than situps or crunches could ever do. You can look up a bunch of these online since they're kind of hard to describe.
Starting these at least 4-6 weeks before going snowboarding will put your body and legs in amazing shape for all day riding. My favorite of these was the indo board squats, they're fun and they really do help with your balance more than anything else I've tried.