He sent people to the Gulag and executed people without much regard but, did this apply towards children too?
In 1935, Article 12 of the Criminal Code was passed where kids of the age of 12, most of whom were orphans, street urchins, runaways, or kids that were arrested alongside with their parents were to be tried as Adults and sent to Gulags instead of the camp nurseries. They can suffer the same fate as any other person in the gulag, and the younger children in the camp nurseries were not better off as they all faced almost as bad conditions as the Gulags, such as they often stayed in old barracks that were near freezing cold with barely any heating source (an example being two kids slept in a oven after the coal was finished burning because it was warm inside), eating wasnt a treat or something good it was a form of punishment ,nurses would feed the children scalding hot food and often left them sitting for hours on their potties causing many to suffer from prolapsed rectum, they received inadequate food and nutrition , the nurses gave little to no attention to the kids, they were often abused, some of the children were so neglected that they couldnt speak any language and instead communicated through either grunting or some form of making noise such as the notable case of Genie the wild child, and these camps for the kids were surrounded by barbered wire and guardhouses. Also the camps were on the lowest priority on every camp commanders list. Stalin had no regard of the kids and what the adults suffered the children suffered the same.
Sources;
"The Disparaging Cycle of Children in the Nurseries, Children's Homes, Special Regimes, and Adult Labor Camps of the Gulag." The Disparaging Cycle of Children in the Nurseries, Children's Homes, Special Regimes, and Adult Labor Camps of the Gulag. N.p., n.d. Web. 08 Sept. 2015.
"'The Littlest Enemies': Children of the Stalinist Era." The View East. N.p., 21 June 2012. Web. 08 Sept. 2015.
Stalin never sent anyone to Gulag in fact. Political repressions were administered through ordinary or extraordinary ('troikas') but still legal procedures. Personalizatyion is also not helpful for understanding of historical events. For example you realy can't make clear distinction between Stalin's repression and non-Stalin's repressions. Where is the border? 1924? 1930? Since this term can't be clearly defined it's counterproductive to use for serious analysis. Regarding children. There was special legal status for childeren and spouses - memebers of family of a traitor to the Motherland ( Chapter 6, article 58-8 of Criminal Code of RSFSR). Spouses were usually jailed for 5-7 years. Children sent to state orphanages.