We are going skiing at the weekend. This is correct, and it is the present continuous tense used to talk about a future arrangement. There are many sports and activities that are described in this way: going skiing, going snowboarding, going swimming, going sailing, going horse-riding, going surfing, going hang-gliding. ..... the list is endless. Technically, you could use the 'going to' future with these expressions e.g. We are going to go skiing at the weekend. but the repetition of the 'going to go' is clumsy, so we tend to use the present continuous more. And to answer your second question: No, I'm afraid that 'We are going to skiing at the weekend' isn't correct. Sorry, but you can't say that. 'We are going to ...' must be followed by an infinitive form, not an '..ing' form.