It's not pretty, but this was my setup for a tri-modal (bike, hike, ski) trip I did last winter. I bike with skis fairly frequently because it's often quite some distance to a ski trail. Sometimes skis can be strapped to the top tube, sometimes it's better to sling them across your back.
If you try a sled you'll need to have some type of rigid pole system. If you're feeling rich you could try a Chariot child trailer with ski kit.