Hi!
The best you can get in terms of "downloading the wikidata ontology" would be to download all properties and all the items representing classes. We currently don't have a separate dump for these. Also, do not expect this to be a concise or consistent model that can be used for reasoning. You are bound to find contradictions and lose ends.
Also, Wikidata Toolkit (https://github.com/Wikidata/Wikidata-Toolkit) can be used to generate something like taxonomy - see e.g. http://tools.wmflabs.org/wikidata-exports/rdf/exports/20160801/dump_download...
But one has to be careful with it as Wikidata may not (and frequently does not) follow assumptions that are true for proper OWL models - there are no limits on what can be considered a class, a subclass, an instance, etc. Same entity can be treated both as class and individual, and there may be some weird structures, including even outright errors such as cycles in subclass graph, etc. And, of course, it changes all the time :)