Anonymous
No.
One of the most common misconceptions is that Saiyans can breath in space because the anime features more than 1 scene of a Saiyan being in or close to space and showing no difficulty breathing.
This however goes against the canon fact that Frieza, while fighting Goku, stated that once Namek explodes then he'll have won regardless if he manages to beat Goku before it or not.
The reason: "I can breath in the vacuum of space, while you can not."
Goku didn't reply with anything like "Yes I can" or anything else so we can assume he's aware of this and it's true
Another thing to remember is that scenes in the anime that are filler often contradict facts of the past.
When Goku fought Beerus, they were fighting at the top of the world but this was still in the Earth's atmosphere and not in space itself.
Goku wasn't freezing and was breathing in and out. Saiyans can keep their breath longer than normal humans, hence why he could last so long in a place with very little oxygen.
Anonymous
He can now. Or Akira Toriyama made some mistake when he made Battle of Gods. Will actually he did make some mistake in Battle of Gods. Maybe Goku fighting in space is a mistake too.
MagicianTrent
No, though Saiyans are supposedly able to hold their breath for long periods of time even while fighting .
Quinn
no he cannot