Una hielera can have several translations. Mostly, it's any container that holds ice cubes, with the understanding that the container is portable.
hielera = cubitera
ice bucket
ice cooler
ice chest
cooler chest
cooler
Because these items are portable, they're too small to be a refrigerator.
There are several words in Spanish for a refrigerator, but hielera isn't one of them.
All that said, some in Texas use hielera to mean the freezer compartment of a refrigerator. As I understand, they will add portátil to mean an ice cooler/chest. However, regional usage (in South Texas) makes it right.
I'll defer to someone who lives in Mexico (I would guess the northern parts) to provide a definitive answer to your question.
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