Grace is reportedly a relative of Ziggy, the Danish royal's much-loved family pet of 12 years who died in 2017.
A follow-up snap showed the stunning brown and white Border Collie casting a pensive gaze into the distance, while the Swiss mountains form a picturesque backdrop setting.
Another sweet pic shows Mary’s nine-year-old son, Prince Vincent, resting in the snow alongside Grace, who appears unfazed by the wintry weather.
While Mary is believed to have taken the photos, another cheerful pic shows the princess on the other side of the lens, posing alongside Grace.
A final snap shows Grace casting yet another pensive gaze towards the camera lens.
Enthusiastic fans were quick to take to Instagram to comment on the happy family snaps, with one person writing: “Absolutely gorgeous doggo!!”
Another person stated: “Denmark is fortunate to have such a wonderful crown princess (and Mother) representing them. Bravo!”
A third person added: “Enjoy your stay! It is always a wonderful pleasure to relax on the snow.”
Mary is living in Switzerland with her brood – Vincent, Christian, Isabella and Josephine – who are conducting a three-month exchange at Lemania-Verbier International School.