check dipstick .. see if its foamy/has coolant on it. also a compression check and leakdown will tell you pretty much whats going on... blown HG's dont always leak oil down the block or spill coolant into the pan. sometimes its cyl-to-cyl. which you will be able to easily tell with the above mentioned tests.

I'd also check fuel pressure... might be a shot pump.

i had an 89 Integra briefly and the igniter went out on me in the middle of winter in a blizzard. so i'd check the igniter and coil too... might be a likely suspect. on my teg it would crank and sputter for a couple seconds.. die. replaced the igniter in -20 degree weather and it fired right up.

another reason id sight the igniter is they are classic for starting up cold and then NADA when its hot.