Does red pepper help chickens lay in the winter if so what would jalepenos do for them or any other hot peppers Chile powder etc?

Studies have been done since the early 1940's in Japan, the Caribbean and elsewhere.

While the feeding of hot peppers and vegetation containing high amounts of capsaicin does not seem to bother the hens the only benefit appears to be egg shell thickness. Egg production is NOT significantly effected. The influences of dietary red peppers on daily food intake are negligible in egg production and minimal in yolk color according to the Roche color fan. Adipose tissue weight was somewhat effected and suggests a winter diet of red peppers over 1% of total feed in cold climates may be adverse.