Growing any kind of fruit here in Northern New Mexico is difficult because we always get a cold blast after summer like temperatures in April. Spring always arrives early here in April and all the fruit trees start to blossom. Then a cold blast comes in at the end of the month ruining any chance for fruit. My fig trees are in buckets so I will have to bring them in when that happens. I do have one tree in the ground that is well protected. If it starts to sprout  new growth early, I won’t be able to move it. Luckily it is in an unheated green house and I might be able to protect it. So my question to you all is: How will the trees do if hit with sub freezing temperatures after they sprout new growth? Is there any chance of getting fruit that year?

A late spring hard frost happens almost every year in my area.  Found that the unprotected new growth will likely be killed. 
The fig tree itself will be slowed down but then should continue to grow.
That year figs may start a little later depending on summer weather/heat.

We expect frost until the last third of May and direct frost always kills new growth that slows down the growth process as Pino just mentioned. However placing some fabric (cotton) sheet on top of the plant overnight and removing it in the morning can save the new growth. The direct frost on leaves is the killer. Placing plastic sheet directly on the plant and not removing in time before the sun heat can also burn the new leaves. To cover many plants, when frost is expected, I use a tarp that is kept high not touching the plants

My Vern's Brown Turkey was hit with a late frost in May and it did not produce and figs that year, except a few rubbery ones. This tree is in a pot and I covered it with only a sheet. The frost went through the sheet and killed all the leaves. Another fig tree I protected with a sheet and then a tarp and it was fine.

Now I have a green house plus an area where I setup a tarp to shelter the trees from frosts. It work
wonderfully as I don't lose too many brebas.  There was one year, I lost almost all brebas due to an artic outflow in mid spring that lasted 5 days. All new green growth were killed.