Accessing a IOTA node via Tor (e.g. from a Light Wallet) is possible, since it only requires access to the API port (which is HTTP or HTTPS). However, no current light wallet implementation exposes Proxy Settings to the end user (so he could add his tor proxy). As the wallets are basically a webapp bundled with a Chrome browser, it should not be hard to add it though.
Exposing a full node under an .onion address (in addition to the public address) for wallets to use is also possible (just HTTP).
However, running full nodes (iri) via Tor is not possible. The problem here is not UDP (Full nodes can talk to their neighbors via TCP as well) but the fact that iri expects all traffic to originate from the IP addresses of its known neighbors (and being able to connect back to them). Public Tor exit nodes will not be valid IOTA neighbors.