My Italian EB, Hardy Chicago and Petite Negronne have finally started to leaf out. They were set out in late April after spending the winter in an unheated shed. I think it must have been too cold in there as 2 Poms never made it.
Would it be wise to keep these figs growing in my greenhouse this winter to gain strength and then allow them to go dormant during the winter of 2015?

If you have a greenhouse, it might be a good idea to use it for these figs. Either it was too cold as you noted or perhaps they dried out a bit too much. A winter in a greenhouse should help

Rich,

    I don't know if this is relevant, but I started some last year and let them winter in my basement under lights. I took them out in the spring and they just sat there. They didn't break bud and start producing new leaves until late June. The figs left in the garage for the winter broke dormancy starting in April.

    This doesn't answer your question about greenhouses, but is  just my Zone 6b experience.

Rich,
I had a similar situation with several cultivars including several Hardy Chicago. They were left outside too long (an experiment) and experienced temperatures below 15 deg F. (the roots were frozen solid). Several plants that were better protected, started to leaf out in April, while the few that were frozen had die back, have lagged behind and are just not starting to grow (2 weeks ago).
IMO, I would let them grow as much as possible now, let them go dormant and store them in a protected location above freezing for the winter. Young plants from last year (1 gallon with lots of tender growth) that were kept above freezing but dormant, have put on a tremendous amount of growth and are producing figs this year.

It depends on your set up.  If you can keep night time lows over 60 and daytime highs over 70 the figs will still grow.  But you have 2+ good months of growth left so letting them go dormant in Oct would be OK, too.  Fertilize them with immediate release fertilizer until early to mid Sept, leaving at least 4 weeks from last fertilizer application until the figs start to go dormant (night time lows under 50)