Is vinyl click-plank flooring appropriate for 3-season rooms in cold climates?
if you look at the manufacturers directions for the flooring it will tell you what temperature limits your flooring can take. For example: 


  Make sure the temperature in the home is maintained between 65F to 80F
  year round.


If you are worried about temperature extremes consider something else like ceramic tiles. Another thing to keep in mind in our climate is that for a sunroom you want a flooring that can absorb heat during the day and release back heat overnight to keep the room warmer in spring/fall and cooler in summer. Click-vinyl plank flooring is not good for that compared to other material such as ceramic.