There is an interesting article which I could not get to paste here, but you can look it up on
www.flightsafety.org/alar/alar bn8-6-wind.pdg
The maximum demonstrated crosswind published in the approved airplane flight manual (AFM), aircraft operating manual (AOM) and/or quick reference handbook (QRH) is the maximum crosswind component that was encountered and documented during certification flight tests or subsequent tests by the manufacturer.
The wind value is recorded during a time period bracketing the touchdown (typically from 100 feet above airport elevation to when the airplane reaches taxi speed).
For some aircraft models, if a significant gust is recorded during this period, a demonstrated gust value also is published.
The maximum demonstrated crosswind;
1. is not an operating limitation (unless otherwise stated);
2. Is not necessarily the maximum aircraft crosswind capability; and,
3.generally applies to a steady wind.
Much more information is included in the article.
Of course the crosswind capability is affected adversely the several factors.
The Westwind for example has a demonstrated component for the Westwind I of 20 kts. The Westwind II is 23 kts. No major differences in the two aircraft. So if you fly the westwind 1 at 23 kts crosswind, you have not become a test pilot. It was never meant to be a limiting factor for design purposes, thus it is no different than climbing out @ 15 kts over recommended climb speed.
In fact it could be that a crosswind of far less than maximum demonstrated is extremely risky on an ice covered runway.