Can Slopes Import My Data from Other Apps/devices?

Yes, along with being able to use Slopes to record, you can import data from other devices and apps. Slopes supports the common GPX file-format, and some app-specific formats too.

There are multiple ways to import your existing data:

Note: Slopes as an Open In destination has a chance to be broken by iOS 13 when it comes to GPX files depending on what other apps you have installed. This issue is breaking many apps with GPX imports, not just Slopes. There is a whole thread of us outdoor-activity app developers being told by Apple that there is nothing we can do to immediately fix the issue. I've followed their suggestion and included it as part of v2019.16. Airdrop will work fine, but Slopes will not be guaranteed to be an Open In destination from the share sheet when you:

Email the file to yourself, tap the attachment, and pick "Open in Slopes." Slopes will process and import the GPS data as an activity.
If you've saved the file to your iCloud Drive, you can hit the plus button in the top right of the History tab to bring up the document picker to import it.

What I have found that fixes it, although I'm not recommending it, is that the issue stems from multiple apps saying they can import GPX files, but having slightly different definitions of what a GPX file is. I had to delete all the outdoor-activity-related apps that did show up as an Open In destination for GPX (but not generic apps like Dropbox), look at the share sheet and do it again for the new apps that appeared for GPX, and Slopes finally showed up again.

My official recommendation is to just use AirDrop from another machine...

If you have more than one file to import:

You can AirDrop all the files at once from your computer. Drag all the files onto your phone in the finder (via the AirDrop folder in the sidebar) and pick Slopes on your phone.
You can also use iTunes File Sharing to import a bunch of activities at once, too. Follow Apple's guide to get started.

Exporting from Ski Tracks

Files exported from Ski Tracks in the .skiz format can be imported to Slopes.

Exporting from Snoww

Snoww lets you export to GPX, which Slopes can import.

Exporting from SnoCru

Sadly SnoCru does not provide a way to export your recorded data.

Exporting from Trace / Alpine Replay

Trace can export GPX via their web interface. Head to http://snow.traceup.com/settings/gpx, log in, and then you can pick which days to export.

GPX Import Requirements

GPX files are commonly exported from other stand-alone GPS devices (such as a Garmin). Note that the file needs the following data to be included: latitude, longitude, altitude, and time. Data accuracy is improved if the file also contains vdop and hdop (vertical and horizontal accuracy) data.