Not necessarily. It's not as simple as just lowering the temp at which the thermostat opens. In a cooler region, or during winter, it will usually lower the operating temp of your engine. However durring warmer periods, or when your engine is working harder, it could acutally cause your engine operating temp to rise. "How can that be possible?" I'm glad you asked
Heat Transfer is is nothing more than transfering waste heat from the source (your engine) to a heat sink (the air around). For heat transfer to occur, there has to be a temperature difference between the source and the sink. Also, the greater the temp difference between the sink and source, the greater the heat transfer rate. ie: A glass of water at 200 deg in a room that is 70 deg will take less time to cool to 150 deg than it will to cool to 100 degrees (assume the room stays at 70 deg). This is an exponential function.
Now, lets apply that to your engine. We'll start out w/ your engine (source) at 70 deg (summer morning, all parts/fluids are at equal temp) and you are using an 180 deg thermostat. You start up your engine. Immediatly the water in the cylinder jackets and heads starts to warm up untill the water at the thermostat reaches 180 degrees (we'll assume for simplicity's sake that all water is uniform in temp). The water in your radiator is still at a cool 70 deg. The hot and cold water quickly exchange places due to the water pump untill the water at the thermostat is at some temp less than 180 (we'll use 170. A thermostat opens at one temp, and closes at another, slightly lower, temp). The 70 deg water is then heated as the 180 degree water is cooled in the radiator. (Side note: heat transfer from fluid to air (via radiator) is a much less efficient process than from the engine block/heads to the water.) This process continues untill you shut off the engine. Assuming that the outside temp stays the same, and the air flow (cfm) across the radiator is the same during the time the engine is running, a certine amount of heat is transfered from the engine to the air over time (BTU/hr).
Now, lets assume the ony thing changed between the above and this run is the thermostat. The air is still 70 deg, the airflow over the radiator is the same, the engien is under the same load conditions w/ the same efficiency. You now put in a 160 degree thermostat (which closes at 150). The cycle above will still occur, however it will occur more frequently. Once you are in the cycle, w/ water exchanging at 160 vice 180, more heat is being transfered (at least initially) to the water. Good, right? Well, hang on and see what happens. This now cooler (than the pervious example) water enters the radiator. Since it is at a lower temp, the rate of heat transfer (BTU/hr) is a bit lower. Howver, the heat transfer rate to the water in the engine is higher. The water stays a shorter time in the block to heat to the same temp. The water is then staying in the radiator a shorter amount of time, and is not cooling as much (total amount of BTU tranfered to the air is less) as before. Now when this batch of water enters the engine, its hotter than initially. It is much closer to the 160 than it was before. Now even less time is spent in the block to absorb the heat. Eventually this will lead to water remaining above 160 deg, and constantly cycling through the engine and radiator. At about 250 deg, the radiator cap will lift and you will have a boil over (assuming a 15 psi cap).
If your radiator is efficient enough (big enough, larger capacity fans, etc), this may not happen, and your engine will operte just fine. But if you cooling system was designed for a 180 deg thermostat, you will want to consider its heat removal capacity before changing your thermostat to a lower temp. Here in New England, you may be able to get away w/ the change, but if you move to a hotter climate, probably not.
Just my $0.02
