Isn't this fairly typical, though? I mean, sports which require some kind of expensive equipment tend to favour wealthier countries and disproportionately favour the financially well-off within those countries too. It's perhaps no surprise that developing countries are more easily able to bridge the gap to the wealthier countries in the sports that don't require such significant financial investment from their participants than in things like sailing, cycling and equestrian as a result.
The other thing that needs bearing in mind when looking at these medal counts, also, is that you have to remember that many of the countries above Germany in the medal table don't see their Olympic sports funding needing to be split across summer and winter games quite so evenly - only really Russia and the US are direct competition in that respect, and they have the financial might to be ahead of Germany anyhow. Japan has some wintersport interest, but this tends to be in specific disciplines (ski jump, for example) as they are peripheral nations in many of the other events, plus they will have invested more heavily in this Games as the host. The Dutch - and I know it hurts to be behind the Dutch on the medal table (Germany had more total and the same number of golds, but the Dutch had an extra silver) - only have one sport they pay any heed to in the winter Olympiad, although like the track cycling being focused on by the British, it does have a high number of medals in a fairly shallow pool of competition. Across a combination of both Summer and Winter games (going by position rather than total medals, as there are far more available in the summer games), Germany rank 2nd across Pyeongchang+Tokyo, after the USA - although of course this is not the easiest of cycles to fairly judge the Russians on due to the politics and controversies surrounding eligibility of athletes especially at Pyeongchang.
In the US the federal (even state governments) don't really finance sports. The bigger sports you can start participating in in Jr High or High School depending on what sports the school you are going to offer (sometimes even elementary school). Then of course we have the colleges with their different sports programs. Some cities have city leagues for different sports, others don't. As for Olympic financing that is basically through corporate sponsorship. There are so many commercials that include the tag of Official Sponsor of (fill in the blank).