Can a character in the Sacred Fist prestige class use the Ice Gauntlet and Ice Axe spells without violating their vows?
The Code of Conduct of the prestige class sacred fist (Complete Divine 59-61) says that a creature that joins the organization "refuses to use any weapon. A sacred fist who knowingly carries or uses a weapon loses all class spells and features and advances no farther [sic] as a sacred fist until he atones." Given the prestige class's class features and rather than assuming the organization forces its members to undergo multiple amputations, this DM assumes that by weapons the organization actually forbids its members from using and carrying weapons that are not natural parts of the member's body. (That is, unarmed strike is an entry on Table 7–5: Weapons (Player's Handbook 116-17), and even a nonmonk's unarmed strike "may be a punch, kick, [or] head butt" (PH 121).)
The 1st-level Clr spell ice gauntlet [evoc] (Spell Compendium 119) says that the caster "can attack with [his] fist in all respects as if [he] were wearing a +1 spiked gauntlet." As attacks with the spell's effect remain attacks with the caster's fist, this DM would rule that a sacred fist could indeed employ the ice gauntlet spell's effect yet still remain in good standing with his organization.
However, the 3rd-level Clr spell ice axe [evoc] (SpC 118) says that the "spell creates a battleaxe-shaped formation of jagged, fast-swirling ice shards in your hand. You are automatically considered proficient with the ice axe. Attacks with the ice axe are melee touch attacks." The description of the effect and the fact that attacks are made with the actual ice axe effect itself combined would see this DM rule that the ice axe effect is, in fact, a weapon, and that employing the effect violates the organization's code.
However, in both cases, I recommend asking the DM. The line between spells and spells that are also weapons is blurry, and another DM may have a different but totally reasonable reading of the spells or the sacred fist code.
Based upon the exact same information (https://dndtools.net/spells/spell-compendium--86/ice-axe--3862/ & https://dndtools.net/spells/spell-compendium--86/ice-gauntlet--3882/) as @Hey I Can Chan, I'd rule the exact opposite.
In my humble opinion the ice gauntlet is an armed melee attack doing some extra cold damage, thus forbidden.
The ice axe however, is a spell-effect doing cold damage upon a successful touch attack. As it does no melee damage whatsoever, I'd rule this as an unarmed attack.
edit +1 for the comment made by @gaynorvader (ask a patron in-game).