A lot depends upon the size and structure of the organization, and the person or people in charge of setting company-wide policies and their general disposition (i.e. are they dictators, or collaborators).
In smaller organizations/startups a great deal will depend upon the founders' personal preferences and overall approach. If they're despotic, then the culture will be whatever they decide, for whatever arbitrary reasons they feel like (and trying to enact change from within will generally be futile). If, on the other hand, they want to set up a more egalitarian kind of environment you'll get something that's influenced by the ideas and preferences of everyone involved. You may even get some rationality in terms of which features are picked and for what reason(s). The latter case is relatively common with tech startups.
In larger organizations you'll see less influence in terms of individual preferences and both 1) a greater tendency to simply enact the conservative/pragmatic/"safe" option (nobody wants to leave themselves open to taking the blame for a well-meaning policy-change that has unforseen, disastrous consequences) and 2) a much stronger resistance to change/new ideas.
As you get more people you run into issues like "'Bring your dog to work day' seemed like a good idea, but John is allergic and Sue keeps saying that 'if dogs are okay then cats should be too', and Pete wants to bring his snake, so the simplest way to solve all those problems is to not have 'Bring your dog to work day'"; so policies/cultural aspects that might actually enjoy popular support even amongst the leadership may be decided on the basis of practicality/fairness as opposed to anyone's personal preference or rational argument.
So at the end of the day, it depends. And it's not always one or the other. In any organization there may be some cultural aspects that the leadership (rightly or wrongly) considers of critical importance and so they mandate accordingly in those areas. And there may be other aspects that they don't really care about (or notice/think about), which then get decided by popular opinion, rational discourse, or similar mechanism.