Nitrile gloves aren't suitable for working close up with really hot objects. Bare-handed if you accidentally brush against the barrel or bit of your iron, you will feel it quickly enough to react before you get more than a very small burn. in most cases if you make contact with any part of your hand with thicker skin, you'll get away with no more than surface scorching and no blistering.
However, as soon as you add rubber/plastic gloves, any burn will involve melted plastic that sticks to your skin and vastly increases the heat transferred and thus the damage. Also any blobs of molten solder large enough to melt throuugh the glove will be stuck to your skin till they cool or you manage to knock them off.
The risk can be mitigated to a large extent by wearing gloves made of a heat resistant fibre or thin leather over the ones providing the chemical barrier, but their extra bulk makes it very difficult to do fine work.
If to meet quality standards for surface contamination, you *HAVE* to wear gloves, you need to be a lot more careful. It also makes it far harder to manipulate really small parts, so will have a significant impact on your productivity. The only other reason to wear gloves is if you are in the repair trade and working on personal devices, as the user contamination in them can be pretty gross, even if your counter staff are trained to reject repair jobs that are obvious bio-hazards.
Finally: *NEVER* smoke cigarettes while working with SnPb solder. Solder dross will get transferred from your hands to the cigarette paper and burnt, and you will end up inhaling fine lead oxide particulates and organolead compounds from the oxides reaction with the tobacco pyrolysis products.