The 33-year-old shared a selection of photos of herself out in the snow at Pickle Cottage with three-year-old Rex and one-year-old Rose.
While most of Solomon's five million followers enjoyed seeing the star share a family moment, OK! reported that some posted hurtful comments about the fact Rex wasn't wearing a hat while she and Rose were.
In the caption to the post, Solomon said she and the family "woke up to what seemed like Narnia outside the window" at their Essex home.
She added: "We made the most of a very, very rare snow day and spent all day in Joes childhood sleigh that he has had since he was 10, making snow angels and having snowball fights.
"It was such a special day that none of us knew was coming."
One of Solomon's fans hit back at the trolls in a comment on her post, writing: "I think it’s disgusting that people feel they have a right to dictate on how anyone should let their kids play."
Many also pointed out the difficulty of forcing a child to wear a hat when they don't want to, regardless of how hard parents try.
One commenter wrote: "Right keyboard warriors, who all think they are the best parents going, let @staceysolomon live her life without judgement or criticism from anyone.
"It’s memories she’s making with her children. Leave it out on her children or what they are wearing. It’s nobody's business, full stop."
Solomon has been on TV screens over the festive period, presenting Stacey Solomon's Crafty Christmas on the BBC, offering ways to add homemade charm to decorations and gifts.
The programme features Solomon and husband Joe Swash working on various festive craft projects, with their children getting in on the act too.
Watch: Stacey Solomon shares glimpse of fairytale wedding