Hi, there is no difference. I don't like the word like, so rather use the word enjoys, but then your sentence would be "My sister enjoys ice skating"/ "My sister enjoys to go ice skating."

There is a slight difference between them. She likes to ice skate = she enjoys skating on ice She likes to go ice skating = she enjoys going to the ice rink - or to a frozen lake - to skate on ice. This might mean eg an evening out with her friends at the ice rink. It's more of an 'activity', and perhaps a social occasion too. By the way, there is also a difference between the way that American and British people express this idea. When we talk about activities that we enjoy in British English we say 'I like + ... ing' (gerund form) : eg 'I like ice skating' . Americans would use 'I like to ice skate' ( to + infinitive form). NB the verb 'enjoy' is always followed by a gerund eg 'I enjoy ice skating ' ' I enjoy going ...' I hope that helps.