Since you are in a climate where they can go outdoors most of the time (no Canadian winter
) then as long as they have good sized patches of SHADE in the run, I doubt you are running any much more risk of problems at 3 sq ft per hen than you would at 4. The only thing is that, as another poster points out, if problems start, what do you do then?
Just one other comment: 14+ hrs a day of light does help maintain winter egg production in typical breeds (a number of the sexlink lines seem to be so production-bred, though, that they don't need it -- I have 2 ISA Browns that gave me nearly an egg per hen per day all winter with NO supplemental lighting, even though December days up here are NOTHING like 14 hrs long). However I am not so sure about your suggestion that it is 'good for their health'. There are some fairly reasonable reasons to believe that laying all winter is probably NOT in the hens' best interest, healthwise. (Of course if like mine they do it on their own there is nothing you can do about it). So, I would not personally suggest giving supplemental lighting unless you really want a few extra eggs. Mind, there does need to be reasonable natural light in the coop (IMO) but I don't think you need to *supplement* it.
Have fun,
Pat

Just one other comment: 14+ hrs a day of light does help maintain winter egg production in typical breeds (a number of the sexlink lines seem to be so production-bred, though, that they don't need it -- I have 2 ISA Browns that gave me nearly an egg per hen per day all winter with NO supplemental lighting, even though December days up here are NOTHING like 14 hrs long). However I am not so sure about your suggestion that it is 'good for their health'. There are some fairly reasonable reasons to believe that laying all winter is probably NOT in the hens' best interest, healthwise. (Of course if like mine they do it on their own there is nothing you can do about it). So, I would not personally suggest giving supplemental lighting unless you really want a few extra eggs. Mind, there does need to be reasonable natural light in the coop (IMO) but I don't think you need to *supplement* it.
Have fun,
Pat