Fire snakes can cause problems if they are frightened. This can happen if you have a perfect storm scenario-- Say, your fortress has been carved into bituminous coal, or some other flammable material-- There is a non-filtered magma pipe fueled workstation nearby, and there are TONS of cats in the fortress.
Firesnakes are vermin, so they spawn and wander about. Cats are drawn to vermin creatures. Firesnakes can cause fires when they get attacked. If the cat attacks the snake, while it is on the bituminous coal floor, the floor MAY catch fire-- or some other fancy thing may happen, like the cat catching on fire, and then wandering into the stockpiles to hunt other vermin (while on fire), and catching other things on fire.
For the most part though, the most harm a fire snake tends to do is give somebody a "hated vermin" type bad thought when they see it. Same as seeing a giant roach or something.
Now... Magma crabs, and fire imps? TOTALLY different kettle of fish! Those guys are THE REASON why magma plumbing NEEDS, (and I stress that very much, it is a *NEED*!) to be filtered using some fortification slits, at the very least. (For workshops that dont actively draw up magma, active isolation is the best!) Fire imps shoot fireballs-- literal fireballs-- at dwarves on sight-- and Magma crabs shoot an inexhaustible supply of bassalt boulders at dwarves on sight. Both are pernicious and deadly. They can end your picnic REAL quick. (On the plus side though, if you can CATCH them, and then train them-- *hah!*-- Fire imps on chains make GREAT anti ambush defense systems! Just make sure that your fortress's above ground walkways and perimeters are fully able to be locked down quickly, because fire imps WILL set the world on fire. This can be a GOOD thing, if you want to burn up all the ambushers. Just be sure you can lock the fortress down before the fire gets inside and kills everything/everyone.)