I'm curious if the nitrogen fixation is done by symbiotic bacteria.

If so, can both organisms survive in all the climates where cattle is raised?

Yes, legumes are fairly unique in that their root nodes host symbiotic bacteria capable of fixing nitrogen for the atmosphere. That's why they are so important in crop rotation or polyculture.

Every region could have different species that work best. The finding of this study, as I understand it, is identifying this foreign species that happens to work well for the location and agricultural needs.