Hi Joolz,
A quick look at the history of the Winns of Nostel shows that they descend from “George Wynne of Gwydir (who) was appointed Draper to Elizabeth I”. In turn the Wynns of Gwydir claim descent from the royal house of Gwynedd, one of whose emblems was, supposedly, an eagle “displayed”.
Whilst the College of Heralds had been established in 1484 it had no real powers over existing heraldic symbols until authorised to undertake visitations in 1530. Up until then heraldry in England was unregulated, and individuals were free to adopt whatever designs they chose provided that they met the generally accepted conventions on colour and design and were not a direct copy of somebody else's.
To confuse the issue further, heraldry in Wales, which was not subject to English law at this time, had developed some idiosyncracies of its own. In particular, because of the tradition and strength of genealogical recording, where families claimed descent from an illustrious ancestor, that ancestor was ascribed symbolic arms. Thus Owain Gwynedd (d 1170) was alloted the eagle, amongst other insignia, although there is no evidence that he actually bore this device. Some families descended from him then used the eagles to signify their connection ( For example “Vert,three eagles displayed in fesse Or” in the arms of the Aberffraw branch)
It is possible, therefore. that your Winns,although not closely related to the Nostel Winns, were also of the house of Gwynedd and chose to use the eagle as an emblem accordingly. Certainly the surname suggests a Welsh origin and you may want to try that line of enquiry further.
Maec