This whole mess kicked off when the 'GoT' star recently shared IG snaps of herself hitting the slopes with her boyfriend, Peregrine Pearson, and their pals ... writing, "Jägerbomb anyone?" Clearly just a fun post showing her enjoying herself and living her life ... although, trolls felt very differently about it, and they let her know en masse in her comments.

Unfortunately for her, there was intense outrage over Sophie having the audacity to enjoy some downtime without the presence of her kiddos -- especially since her last few months have been rife with Joe Jonas divorce drama.

Her comments were rife with questions about children's whereabouts -- with some demanding she oughta "be a mom" -- and while ST reportedly attempted to delete some of these remarks, some still filtered through ... and other fans jumped to her defense.

One loyal supporter put out a reminder that women were allowed to have an identity outside of being a mother -- and another called out the sexist double standard ... saying there was no kid-related outrage over on JJ's IG.

Others pointed out that in a custody agreement situation, a mother has free reign to go out and enjoy her life when she didn't have the kids -- not be locked away from the world while knitting and baking cookies, which the haters seem to think was normal.

In Sophie's case, she recently came to an amicable custody agreement with Joe after months of turbulence put in motion by his divorce filing in September last year.

Things got messy soon after ... Sophie cited a whole "child abduction" law, claiming Joe was preventing their 2 children from traveling to see her in the UK by allegedly withholding their passports -- though she asked a judge to dismiss the claim last month.