Sticking to barrack room law chat for the moment
"If you fly an N-reg in the UK on the strength of an FAA pilot certificate"
a) quite a lot of FAA IR holders also have a valid UK IMCR, so provided they are below Class A they can fly IFR (in IMC as applicable) in UK airspace on their UK license, and
b) on a typical IFR flight to another country, it is not unusual to remain below Class A, or even OCAS entirely, when within UK airspace (for simplicity of routing), and once outside the UK (when any IFR flight will be on the FAA IR privileges) the "known ice" argument comes down to whatever weather forecasting service(s) are applicable to the airspace one happens to be passing through, and what they say about icing...
Weather forecasting services are like the old joke about British Standards - there are so many to choose from
