Have a look through the Warn site they give minimum battery requirements for all their winches

**LINK**

I have a similar winch, just use the car battery, but with the engine running.

I use a separate battery which is carried in the trailer,and keep it regularly charged with one of the small modern battery chargers,I would not use my towing vehicles battery as modern motor vehicles electrics/electronic are so complicated,expensive and all to easily damaged.One suggestion is to use a battery of the same type size and spec as your cars battery,so should your cars battery fail either on the road or at home you can swap the trailer battery onto your car and get you out of trouble. On my big trailer winch which needed a large battery I use the same battery as the one fitted to my tractor,so effectively I have a spare battery which can fitted to winch or tractor should one fail. Be careful when buying a winch ,look at the line speed specification,if the line speed is high your engine will whizz up into the trailer like a rocket. For a 3 inch model why not consider a geared hand winch,very reliable,no flat batteries , cheap. I have used hand winches to load stationary engines for 40 years weighing from 4cwt to 27 cwt with my wife winding the handle and me guiding the engine ,though now with us both now past 70 an electric winch may become necessary on the half ton engines. When I had a 2 ton 6 inch Burrell an electric winch was essential ,though when you get to this size the winch needs to be well over rated for the job, Also look into the synthetic winch cord which is a strong as steel and expensive but sits on the winch drum without springing and uncoiling and no sharp wire ends.

I kept first 1st post brief to suggest a car battery would be fine, but I to use a car battery which I keep in the boot i find this I don't have to 'pop' the bonnet, stretch the leads so far and I also use it to run my steam raising fan.