With the fridge, it's mostly if there is enough oxygen to keep the flame lit...at 6000ft, it's probably not an issue. Flame might run a little longer but it's unlikely to significantly impact cooling. Of course, at high altitude, temps tend to be lower so it's less of an issue.
Generator on the other hand is powered by a naturally aspirated (ie: no turbo or supercharger) internal combustion engine. Generally, they will lose 1% of power per 300ft of altitude(you can find various amounts shown on the internet but generally in this range), so at 6000ft, you will be down by about 20% on power. If you are pulling 500w on a 3000w generator, you probably won't notice. If you are pushing up against the limits, the generator may struggle.