the limit in the POH (which nobody yet seems to have suggested should be consulted)
Of course, consult and follow the POH. Though understand that with very few exceptions, the "Demonstrated Crosswind" value presented in the POH is the crosswind speed required to be demonstrated during certification, and is not considered limiting, unless specifically presented as an absolute limitation.
A part of the thinking on this will be where is the value stated? Using the PA-28-181 POH as an example, Section 2, Limitations, makes no reference to crosswind values, so there is no limitation. It is found (as required to be presented to the pilot) in Section 4, Normal Procedures, 4.2 Airpseeds for Safe Operations, and is expressed as a maximum demonstrated crosswind velocity. Cessna typically presents it in Section 5, Performance, and using the 172S as an example, it says: "Maximum demonstrated crosswind component 12 15 knots (not a limitation).", Which is good news for Chickenhouse!
Interestingly, my taildragger flying boat does contain crosswind limits in Section 2, Limitations, so the pilot is bound by those as limitations. Though its a very early FAR Part 23 airplane, so the refinements of what is and is not typically a limitation may not have been worked out. The crosswind limit for it is greater on the water than on the runway, though generally it's not necessary to land with much crosswind in the water. If the wind is that strong, either land directly into it, or it's too rough anyway! A lesser crosswind limit as a taildragger on the runway is appropriate.