What they can/will do depends on hte rights granted to the HOA in your documents. At the very least, they can sue you to correct the violation, and if found in their favour, you can end up being assessed all costs (your attorney, their attorney, court fees, etc.). They may be able to fine you large amounts, which can accumulate daily.
Some states allow them to file a lien on your property and foreclose on it if not settled within a specified timeframe.
Now these are worst case scenarios; some HOAs will do nothing, or choose an easier path. You see/know how other rules are/aren't enforced; expect any rules relating to poultry to be handled similarly.