Poor Snowflake. While the fam's soaking up the rays, the pooch was left to fend for itself ... according to a New York Magazine reporter who snapped this shot of Snowflake all alone in the Houston home Heidi herself said they desperately needed to escape.

There was a security guard in the driveway who reportedly said he was taking care of Snowflake -- but remember, the Cruz house has NO heat, just like millions of other Texans who are riding out the brutal winter storm.

A few of those folks -- Ted and Heidi's neighbors -- actually scored an invite to Cancun ... based on texts she allegedly fired off before they flew the coop. Reform Austin says it obtained the messages in which she asked a couple neighbors, "Anyone can or want to leave for the week?"

Heidi even told them which flights she was taking with Ted and the kids ... and boasted they were getting rooms at the Ritz-Carlton Cancun for $309 per night. She explained they "couldn't stand it anymore" because their house was absolutely freezing -- and the only alternative was for all the neighbors to huddle together at one friend's house ... who did have heat.

In the end, we know what the Senator and his fam opted to do. Interestingly, Heidi's texts make no mention of their daughters going to visit with friends in Cancun ... as their pops, Cancun Cruz, claimed on Thursday.

Of course, once he returned -- in the face of all the backlash -- Cruz admitted he'd made a colossal blunder in taking the trip.