The former New Jersey governor told Fox News Radio about how Cruz made fun of him for being caught at the beach in 2017 during a lockdown.
Cruz and his family headed to Cancun this week as millions of Texans have been facing freezing temperatures and power outages.
One snowman in Times Square was given a face mask, while some people dined outdoors because of coronavirus restrictions.
The storm system is expected to stretch 1000 miles from northern Georgia all the way up to New England, and could result in freezing rain, strong winds and hazardous travel conditions particularly along the I-95 corridor.
"I really don't see a way out of this for many cities across the Northeast. The No. 1 ingredient: the injection of cold air," said AccuWeather forecaster Bernie Rayno.
A winter storm with snow, severe thunderstorms and strong winds is moving into the central and southern parts of the country before it hits the Northeast later this week.
As the powerful winter storm leaves the Northeast, a new storm building off the West coast is expected to bring heavy rain and mountain snow in California and New Mexico.
More than 200 schools across New Jersey, Connecticut, Albany and other parts of the New England area are closed following severe disruption from the winter storm that hit the Northeast this weekend.
A winter storm warning is in effect across Central and Western New York with a cold front bringing record cold temperatures and snowfall of more than 12 inches in some parts of the region.
The storm has resulted in "heavy, wet snow with accumulation amounts up to three feet in some locations," according to Governor Steve Bullock.
A winter storm unlike any since 1934 could bring more than 50 inches of snow to western Montana and northern Idaho, according to the National Weather Service.
The family survived by staying hunkered down in their pickup truck.
The few inches of snow dropped in the Northeast Monday are expected to melt by Monday afternoon or Tuesday as temperatures rise to the low 40s.
The cold clearly did not bother the 37-year-old Elsa impersonator.
Winter storms of Christmas past have halted cities and airports, buried cars and even caused 34-foot waves on coastlines.
There's a difference between weather and climate.
Parts of the Northeast will see 6 inches.
This map will tell you what your chances are.
Indiana lawmakers' attempt to round Pi to 3.2 and a Pi world record are among the things you probably don't know about Pi Day.
This week was not the first time the governor was faced with the decision to continue with his personal plans out of state or return home.