If you want to use your SKY subscription, the card is "married" to the receiver, so you would have to use your current SKY box & card.
A 12 volt inverter would have to be used. They don't drain batteries quickly, unless you draw many amps. A normal sat receiver only uses 50 watts or there about, so should run all day on a fully charged battery. An old CRT portable TV draws many amps and would easily run a battery down. It just depends on what is connected to the battery.
If your clever with electronics, you could make up a PSU for an old SKY box, but you need various regulated volts feeding different parts of the main board (5-20v)and it's not worth the headache.
There are some 12v sat recievers aimed at the caravan/leisure market, but I've not tried them so cannot recommend.:mecry: