"The snow was heavy yesterday. We both did not go to work."
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昨天雪很大: Yesterday the snow was heavy.
昨天的雪很大: The snow in yesterday was heavy.
下雪 is a verb, "to snow".
雪 is the noun "snow".
When you say "the snow in yesterday", the "snow" here is a noun.
This feels like an odd use of 没有. Is it definitely correct? It feels like a translation from English "we didn't have to go to work".
Would it not mean "all of us", therefore even more ambiguous plurality than 我们？
You are right. Actually it means "all of us". If you want to stress on "both", you can say 我们俩/我们两个人都没有上班。
下很大的雪 lacks the marker 了 (for completion of an action). 昨天下了很大的雪 would be correct.
This is the second time today that I have typed in the exact sentence in Chinese that the computer tells me is the correct answer, but the computer recorded my response as incorrect. Has this happened to anyone else? Twice today, but both times are the first time since I started using this tool.