And how much do our modern Dwarves of Great Mountain Halls and valiant warriors come from Tolkien vs the old Germanic myths?
Because Disney’s dwarfs seem closer to gnomes than Thorin Oakenshield.
/u/itsallfolklore has some fascinating earlier answers about Tolkien's dwarves (much of which applies to Disney as well) versus the beings of folk tradition:
Tommyknockers / Knockers in mines - be sure to check out some of the images in the follow-up comments
Had the 'dwarfs' of Europe been based on Jewish people before Tolkien?
Did Tolkien base his Elves, Dwarves, and Orcs on earlier legends, or did he invent them wholesale?
Some further notes on underground mining creatures in European folk tradition
And /u/AncientHistory contributes some background on literary dwarves (or dwarfs, as it were) pre-Tolkien:
No, none of these says "Q% of Europeans and Americans knew what a dwarf was before they saw Snow White". But you can get a good sense of the overall cultural presence of the little guys (and gals, remember!--don't be deceived by the beards).
I contemplated answering this, but I kept choking on its for various reasons. My thanks to /u/sunagainstgold who has a better handle on my previous answers than I do!
The first part of your question is easy enough: between the Grimm's collection (reprinted in many forms, but even when abridged, Snow White was often part of those books) and Wagner's Ring Cycle of operas, dwarfs in mines were part of the popular lexicon in the English-speaking world of the early twentieth century.
One of the problems with your question is that Tolkien's concept of the dwarves (he preferred "dwarves") changed over time. In his earlier works, unpublished until after his death, they tend to be miserly craftsmen who were far from heroic. We get a sense of that in The Hobbit, at least at the beginning. They evolve into more heroic players as we turn pages and in the Lord of the Rings. But one of the reasons I was reluctant to respond because others can handle Tolkien far better than I.
All that said, there is no question that Tolkien and Disney simultaneously affected popular perception of dwarfs with their two works.