Recent developments in remote sensing have shown that snow depth can be estimated accurately on a global scale using satellite images through cross-polarization and copolarization backscatter measurements. This method does, however, have some limitations in low-land areas with dense forest coverage and shallow snow, which are often found nearby urban areas. In these areas, citizen observations can be fused with satellite-based estimations to deliver more accurate solutions. To that end, we use snow-related tweets that have been annotated by artificial intelligence (AI) methods and are introduced in a novel neural network model, aiming to increase the estimation accuracy of the state-of-the-art remote sensing method. The proposed model combines the estimated snow depth from Sentinel 1 images with the number of Twitter posts and Twitter images that are semantically relevant to snow. The use of instant social media data for purposes of snow depth estimation is investigated, validated, and tested in Finland. Our results show that this approach does improve the snow depth estimation, highlighting its potential for use in civil protection agencies in managing snow conditions.