@wannabemystiker
The main factor is formality. ʌ (written 'og') is less formal, traditionally seen as grammatically incorrect and more used in speech than in writing. 'At' is in fact more used at the beginning of sentences.

The example is a poor choice as it's a fossilized famous quotation.

More relevant:

Jeg skal ud at/og løbe i weekenden.

I would choose og in speech (unless perhaps giving an extremely formal speech). Normal people (perhaps not me) would also choose og when texting. Writing for a newspaper I'd definitely go with at. Or the editor would.

Next example:

At løbe er jo ikke hårdt, når først man kommer i gang.

Being at the beginning of a sentence it pulls toward at. In speech og is fine but at can be used without sounding stilted. At is also likely in SMS.