UPDATE (August 24th, 2021):

Spotify has now started rolling out offline download support for Wear OS smartwatches. Some of the Reddit users have posted about receiving the new feature on their respective wearables. It is reported that the feature is available through the latest Spotify app update. Once the update is installed and a song is played on the smartwatch, the Spotify app shows that information just as it shows for music getting played on any other device.

Original (August 13th, 2021)

It has been three years since Spotify debuted its application for Wear OS smartwatches. It has been a bare minimum application so far but is finally receiving one of the commonly requested features. Spotify has announced offline download support for Wear OS will start rolling out in the coming weeks.

The announcement was made around the same time Samsung unveiled Galaxy Watch 4 and Galaxy Watch 4 Classic. However, it will not be an exclusive release for these smartwatches. It will be coming to all Wear OS smartwatches running Wear OS 2.0 and Wear OS 3.0. This is certainly a good thing for those who own one of the older smartwatches.

Spotify says Wear OS users will be able to download playlists, albums, and podcasts for offline listening. It will allow users to listen to their favorite content without having to rely on a paired smartphone and on an active internet connection. It is specifically beneficial for times when you are out for a run and do not like to carry the smartphone around.

As for the downloading process, Spotify says users will simply need to browse the song, playlist, or podcast through the app on their smartwatches. The next step is to tap the "Download to watch" button and that's it. This will begin the downloading process and you will be able to listen whenever you want.