As you may suspect, both versions are correct. My sense of the difference is that we'd use the "-ing" form to refer to the expedition as a whole. ) If you're taking a short break, warming up in the chalet, you might say to your friend, "Well, I'm warm now.
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AnonymousI'm going to go swimming.The form with -ing is normal. The form without -ing is part of casual speech. This applies to all verbs that follow go in patterns like these.
I'm going to go swim.
CalifJimThe form without -ing is part of casual speech.I read your refs.
Avangi"casual."I use it to avoid having to say "informal" all the time. I get tired of labeling everything "formal" and "informal", which are just two levels of "register". And, by the way, I consider "low register" lower than "informal". These are all my own subjective judgments, of course, and they may well differ from the judgments of others.