The picture depicts the three young boys playing in the snow, dressed in matching outfits.
However, the image was quickly met with negative comments claiming Denise was 'milking' the limelight from her son's death.
'Isn't it sad her other son had to have his day brought down by this being put all over the place,' one social user wrote.
'Yes Daniel passed away and he was his brother and he would of had him on his mind all day. But this is not right,' another added.
A third echoed: 'I was thinking the same thing...let his brother enjoy a day of happiness.'
However, followers also shared their well-wishes.
'Bless all your beautiful children Denise and Bruce. A beautiful family,' one Twitter user wrote.
'Sending love to you and your beautiful family, I think of you often,' another added.
Daniel Morcombe was abducted and killed on the Sunshine Coast, Queensland, in December 2003.
Since their son's murder, his parents have launched the Daniel Morcombe foundation and become crusaders for child safety.