Enhanced acceleration of protons to high energy by relatively modest high power ultra-short laser pulses, interacting with snow micro-structured targets was recently proposed. A notably increased proton energy was attributed to a combination of several mechanisms such as localized enhancement of the laser field intensity near the tip of $1~\unicode[STIX]{x03BC}\text{m}$ size whisker and increase in the hot electron concentration near the tip. Moreover, the use of mass-limited target prevents undesirable spread of absorbed laser energy out of the interaction zone. With increasing laser intensity a Coulomb explosion of the positively charged whisker will occur. All these mechanisms are functions of the local density profile and strongly depend on the laser pre-pulse structure. To clarify the effect of the pre-pulse on the state of the snow micro-structured target at the time of interaction with the main pulse, we measured the optical damage threshold (ODT) of the snow targets. ODT of $0.4~\text{J}/\text{cm}^{2}$ was measured by irradiating snow micro-structured targets with 50 fs duration pulses of Ti:Sapphire laser.