It COULD be the head gasket but maybe not.
Generally (but not always) if the HG goes on both oil and water you will know about it. Water in the cylinder will give you white smoke from the exhaust, oil will give you blue, so unless you are trailing pale blue smoke I doubt it's this but there are some tests you can do yourself.
Get the car so you can reach the large water pipes, start the engine if the pipes go hard you probably have a blown head gasket on the water side. Coolant blowouts can be tricky to diagnose sometimes but you should get some or all of these symptoms:
1. White smoke when starting up.
2. Increased coolant pressure when running.
3. Coolant being forced out of the overflow.
There are 2 more definitive checks but you will need a garage or at least some test kit and carry out a coolant pressure check and a crankcase compression check. Both simple and straight forward but you need the kit and you need to know what you are looking for so a friendly mechanic would be your best option.
I assume you have been topping up the coolant system with water for a bit (no problem in the summer but before the winter make sure you put coolant in it) You may be running a bit of a risk with your water pump, most coolant mixes offer some lubrication as well. The main problem with running on water is you will not find the leak. The coolant gets up to 110-130 in most cars, it stays liquid simply because it's sealed, under pressure in your coolant system. If you get a small leak it will immediately vaporise and disappear as steam, which you may well not see. Coolant also has a die in it so when it leaks it will leave a stain so you can find it.
A few questions:
1: Does the car overheat when the coolant system is full?
2: Does your oil look like; new oil, black or dark tan?
3: How much smoke does the exhaust put out when warm? (You really should only be able to see it fairly close to the tail pipe, by 3 feet it should have disipated)
4. Is there a colour tinge to any smoke?
If it ain't broke, take it apart and see how it works