For that engine there is little danger of damage from freezing even if you left it outside, since the cooling system is designed to be self draining.
HOWEVER: there is a lot more to winterizing than just preventing things from freezing up. As a bare minimum on that engine I would recommend that:
1. You stabilize the fuel and run some stabilized fuel through the engine
2. You fog the engine.
There will almost always be some residual moisture in the exhaust system, and that moisture will cause your valves and piston rings to begin to rust. Yamaha recommends that the MR1 engines always be fogged if they are not to be used for longer than 1 month. Its really easy to do on that ski and takes all of 5 minutes.
For complete winterization instructions for the MR1 engined skis, I made up this list:
1. Flush: Flush thoroughly with fresh water. I run Salt-Away through the system if they have been used in salt and rinse the engine with it. They sell a kit that hooks up to the hose to put it into the system.
2. Change the Oil: Once the engine is hot from the flush change the oil and filter. You want to do this as part of the winterization process. You will need an oil extractor. You should be able to extract around 2.5 quarts on both skis. Put back exactly what you took out assuming the oil level was correct to begin with. The oil level should only be checked when the engine is at operating temperature on both of your skis (dry sump oil systems), and never check the level with the engine cold. Yamalube 10W-40 is best oil. Amsoil Marine 10W-40 is good synthetic choice. Yamaha filter #5GH-13440-00-00 or 5GH-13440-20-00 will work on either ski. Or you can use a K&N 303 on either.
3. Fill and Stabilize: Fill the fuel tank and add Stabil Marine fuel stabilizer. I also recommend adding Yamaha Ring Free Plus fuel additive (1oz. per 10 gal). Now put the bow of the skis up some and run the engines dry for 15 seconds hitting the throttle 2 or 3 times to blow excess water out of the cooling system. Let the engine cool completely (at least 2-3 hours or the next day) then repeat this process to blow more water out and run some of the stabilized fuel through the system. Repeat this process 3-4 times to remove excess moisture. There is no need to add antifreeze to the system. If you do this you can store the skis outdoors with no problems.
4. Fog the Engine: On the FX spray fogging oil into the ribbon assemblies (3 second spray per cylinder on the FX). The ribbon will be 4 round mesh things over the intake. On the VX you need to remove the large hose that runs from the air box to the engine and spray fogging oil into that opening for at least 5 seconds. Now start the engines and let them idle for 15 seconds and shut them off. Fogging is very important on these models (both use an MR-1 engine) and should be done whenever you will not ride the ski for 2 or more months. Water vapor from the exhaust system can corrode valves and rings.
5. Wash and wax the ski: Make sure everything is completely dry inside and out. I use a shop vac to suck water out of the bilge.
6. Apply Anti-Corrosives: Spray anti-corrosive spray on all exposed engine and pump metal parts. I use Fluid Film. Other options are Corrosion X or CRC 656. Spray silicone spray on all plastic and rubber parts inside the engine bay and around the pump (reverse bucket, hoses, etc.). Don't forget to do the mats.
7. Lubricate: Lubricate cables, the reverse mechanism, etc.. I take the handles off and use a cable luber on the cables every year, but if you ride in fresh water you probably only need to do this once every 2 years.
8. Remove the battery and put on a tender: I use a Battery tender junior. You can use 2 of these, or consider one of their multiple models.
9. Crack the seats slightly to allow for ventilation and cover the skis.
10. Don't forget to care for the trailer. If you store the skis outside, I'd put blocks under the trailer to get the tires off the ground. Lube the hubs, spray anti-corrosive spray on metal parts. Dielectric grease on the connectors. Etc..
In the spring put in the batteries then you will want to run the ski on the hose to clear the fogging oil. This is when I change the spark plugs (after that first run). The plugs on these skis are very small and foul easily.........especially after the engine has been fogged. At the very lest pull the plugs and clean them at this point. This keeps the plugs from getting locked into the block. Be sure to torque them carefully (9 ft./lbs), you will snap off a plug if you over torque. Remember no anti-seize on NGK plugs. After you change the plugs you are ready for the first ride........ski is full of fuel, all shined and lubed up and ready to go.
2008 Yamaha FX HO Cruiser
2010 Hurricane Sundeck 2100