
MurphysParadox |

Magic item creation charts and formulas in the book are guidelines to the majority of creations. The book specifically states it does not provide the answer to all possible situations and to consult the GM for doing something more fancy.
Then you go looking for items that already do the function, or come close to it, usually in the area of existing spells or wondrous items. This gives a good idea of the cost.
Barring similar items, the GM makes up a number that feels right based on game impact and player wealth level.
So in this case, Frostbrand is an +3 magic weapon with all kinds of fancy effects. List price is 54k. The math will never work out perfectly because it is a specific weapon, but we can play around with it.
+3 enchantment is worth 18k.
Light is a natural effect 30% of all magic weapons.
Fire resistance 10 is equivalent to a level 2 spell with continuous effect. This is recommend to cost CL * Spell Level * 2000g, or 12k.
So two of the special qualities come out to be 30,000 gold, which suggests the fire dispelling ability costs 24,000 gold... which seems high.
ALTERNATIVELY we can look to the Druid 3 spell Quench, which does the same thing as frostband. If you had a use-based infinite-charge item that performed that spell, it would be 5 * 3 * 2000g = 30,000 gold. On the other hand, it does also damage fire based creatures and works on a far larger area than the sword.
If we scale down the area covered to be just 20' area (like the sword), it is equivalent to a CL 1 version, which would cost 6,000 gold... but that's rather cheap for such a powerful spell
So in conclusion - between 6,000 and 24,000 gold.