The “Browse”-button is visible but doesn’t work when accessing my survey on an iPad, iPhone, Macbook using Safari. When using it thru Window/IE, it works fine.
I have just tested a File Upload question in Safari on my Macbook and also on my iPhone – the browser button worked in both cases.
Are you using a survey with the updated theme designer:
If you are using an outdated theme, that might explain the functionality issue.
I hope this helps!