Can びょうびょう be used to mean the sound of a strong wind? Or does it mean "boundless; limitless; vast; broad" wind?
びょうびょうと風が、耳元でうなった
The びょうびょう you're referring to as "boundless" is [渺渺]{びょうびょう}, usually used as -たる form (形容動詞).
In this context, the word is an onomatopoeia for the howling sound of the wind (note that it has nothing to do with 渺渺). As @ganbare says, びゅうびゅう is much more commonly used for the sound of wind, but such variations are fairly common in onomatopoeic expressions. I feel that びょうびょう sounds more harsh than びゅうびゅう, but it's probably just me.
びょうびょう/びよびよ for the sound of the howling sound of a dog (as @stack reader refers to) is an archaic usage and is mostly extinct today.
I think you might be right and that the dictionary is lacking(which is not rare) by only showing the definition as("boundless; limitless; vast; broad"). I searched many web dictionaries in Japanese websites and it seems that it can be meant as the howling sound of a dog. So perhaps the howling sound of the wind as well.
びゅうびゅう is right. びょうびょう is not common Japanese. Meaning would be almost right. It means too strong wind to go out and keep comfortable.