Not too hard to do - but extrememly expensive and you won't be happy with the results. Running a constant 250 watts off of conventional automotive style batteries is going to mean switching them and charging them every morning, and you must not have 120v power near the batteries, or you would just run the lamp off them, so I guess you would have to disconnect the batteries and lug them back to the house or shop or somewhere to charge them up
I am not recommending you go this route, - but this is what you would need to power a 250 watt heat lamp for 24 hours.
1) 12volt to 120volt inverter (500 watts `100$+)
You will need a 12v to 120v inverter. The price on these is getting cheaper all the time, and a lot of automotive type stores are carrying them now, quality is sometimes a problem, but a heat lamp doesn't need particulary clean power. If you are using a 250 watt heat lamp, you would want to go with a 500 watt inverter at least, most often now the rating on the inverter doesn't reflect the true constant duty cycle.
2) Batteries (22 car batteries 1000$ +)
250 watts at 12 volts is 21 amps, but there is some loss in the inverter, so I would figure for at least 23 amps constant draw on the battery bank. for 24 hours, you would draw 552 amp hours out of your battery bank. You never want to draw your battery bank down more than 50%, and if you want it to last - you will only want to draw it down about 25%, but lets use the more aggressive 50%, you would need a battery bank of at least 1100 amp hours to run your lamp for 24 hours, but then they will need to be charged, so you will need a matching set to swap out while you charge the first set. Figure on at least 2200 amp hours worth of batteries. Your basic 12 volt car battery has about 100 amp hours of capacity, so figure at least 22 of those, plus all the cables to hook them together and to the inverter. If you went with a larger inverter specific battery, you might get up to 250 amp hours out of a large 8D (200+ pounds each!) battery, but very expensive as well.
3) Battery Charger (at least 60 amps 100% duty - at least 100$)
Then you will need to charge up your depleted bank. It was drawn down 50% last night, so you haul the 11 batteries into the back of your truck and take them to your shop and hook the up to the charger, you want them charged by the next morning, so you need a charger that can put the 550 amps back into the batteries in about 20 hours, thats only a 25 amp charging rate, but charging isn't 100% efficient either, so you will need at least 30 amps of constant charging current average to charge those batteries up. Lead-Acid batteries tend to charge hard at first then take a while to trickle up to capacity, so I would figure get at least a 60 amp constasnt duty 12 volt charger. (expensive)
4) Power cables and terminals (100$ +)
Daisy-chaining batteries together to make a big bank gets expensive fast too. You need large enough gauge cable to handle the fast charge rate, which should be higher than the rate of draw off from the inverter. Figure at least 6 guage copper wire to be safe, plus all the terminals to connect to the batteries and the cost of making the cables up.
Look for a better solution, how about a generator with a long extension cord to get the exhaust away from the brooder?
-Ryan