What type of skiing is most similar to street skating? If you ask me, it's not street skiing.
Street skating has always been about taking the ordinary, mundane aspects of an urban landscape and turning them into a playground for creativity. A stone slab becomes a grindable ledge, an empty pool a concrete wave, the subway tracks - a death gap.
Skateboards are at home in the city, and very few spots require a lot of setup. Street skiing almost always requires a setup, usually a source of speed (winch/bungee), and skis are in general pretty out of place in the city. This is part of what makes street skiing so interesting, impressive, and fun to watch, but it definitely places it in a slightly different category than street skating. I think that to ski like a skater, you've gotta shred inbounds.
When I say inbounds, I mean outside the park on runs where people commonly ski. The vast majority of skiers ski past countless features that could be turned into jibs or jumps. With the right mindset, the ordinary features of a typical ski resort become a playground. A cat track becomes a jump, a snowmaking pile becomes a quarterpipe, a fallen tree becomes a log grind. The process of interpreting your everyday surroundings (which as a skier is your local mountain) and creating something amazing is as close to street skating as you can get.
This is something you can do anywhere people ski, not just off the Wildcat lift at Alta. I grew up skiing an 800 vertical hill in Nova Scotia, which to this day struggles to maintain a good terrain park. Most of my days as an early jibber were spent playing on icy snowmaking piles and hitting righteous side bootahs rather than hiking the park, and I'm thankful for it. When you can turn anything into a feature, there's no limit to your creativity.
So keep it skate-style: go skiing outside of the park this year, but don't leave the tricks behind.