How to repair wood carving
Some thoughts.


The big crack on the back looks like it might be amenable to replicating the adjacent area of the coils.  Make a narrow silicone mold of the coils to the left of the crack.  Then position the mold over the crack  and seal it against the snake.  It looks like you will also need to seal off the crack that extends into the base so resin doesn't leak out there.  

Lay the snake with the mold down, and slowly fill the crack with casting resin from the "inside face" of the crack (i.e., the side toward the center of the carving).  Use a syringe to get the resin into the crack, and some tilting, vibrating or tapping, and maybe a thin stick-like applicator or piece of wire to get the resin to flow all the way to the end.  Do this in stages so the resin is free to run through the crack and build up at the far end.  If you add the resin too fast, you may get a trapped air bubble that blocks the resin before it can flow everywhere.  

It looks like there's sort of a dome in the center that's lower than the top of the coils.  Orienting the snake so the mold is down will let the full height of the coils get filled without overflowing onto that dome.  Fill the crack in the dome as a separate step.
That leaves three cracks shown in the pictures -- the head, the dome in the center, and the base under the split in the coils.  Those would be hard to fill with liquid resin because they're curved surfaces and you're working against gravity.

The split in the head is big enough that you may be able to use a hardening filler putty.  The same with the dome.  The type of epoxy putty used for car body repair might be good because it doesn't shrink, bonds to most materials, and can be finely worked.

All three look like they would lend themselves to another type of repair.  Since the split in the head goes all the way through, you would need to seal the bottom of the split during the repair.  The repair method uses baking soda and super glue, which you build up a layer at a time if the crack is too deep to do in one step.  You pack a not-too-thick layer of baking soda into the crack, then saturate it with super glue (use a fine-tipped applicator to get it into the crack without getting it on the rest of the carving).  The super glue reacts almost immediately with the baking soda, turning the mass into a hard plastic.  Do this in a well-ventilated space because it releases a lot of fumes.  If needed, repeat the process to build up the material to the level needed.

The result can be worked with a Dremel tool to restore the matching surface pattern.  BTW, this type of repair can be used on a lot of materials.  It's strong, but a little brittle, so it isn't suitable for repairing things that flex.


Note that any type of repair will not match the finish of the snake.  You would need to add a matching finish (which will be almost impossible, or maybe paint the repairs gold, Kintsugi-style; not a serious suggestion).

Having suggested how a repair might be accomplished, I agree with rebusB's comment that repair isn't really a good idea.  Even the best possible repair will be noticeable and would probably cheapen the appearance.  The cracks are part of its character and history.  Filling the cracks will make it a repaired broken item, and potentially less attractive as art.