If you are thinking about travelling down to see Mt. Doom in Tongariro National Park during the winter, or when it looks cloudy, I would definitely choose an alternate activity. The day we went, we were really unable to get a good view of the mountain, which was the main reason we chose to drive a couple hours south out of Rotorua.
We made the best of it though by driving all around the national park and enjoying what we could see!
If you do risk it, you can actually take the trail up to Mangatepopo Hut located off Highway 47 for a good view.
The Tongariro Crossing is known as New Zealand's Great Walk because it is the most popular one day hike in the country. It is generally a very safe walk, however every year there are people who are unprepared who get into trouble on the mountain. Trampers are encouraged to go in a group and to carry the right equipment. You should take a map of the route with you but it is important to know that the route is marked at regular intervals with the poles with reflective orange markers on them (see the picture). You should keep to the track at all times unless you are carrying a map and know the terrain you will be walking on.
I can't stress this point enough... it is really important to make sure you bring a first aid kit with you if you are attempting to do any hiking/tramping in Tongariro. We used our kit a couple of times... once for Tanya who unfortunately got a couple of nasty blisters on her feet and once for me for a nagging headache I had that wouldn't go away. To try and prevent blisters make sure that you are wearing wool socks, that your boots are comfortable and that you have worn them in. I think my headache could have been altitude and cold related but a couple of Nurofen worked wonders.
In New Zealand the weather can be extremely changeable so it is recommended that you are well prepared for any tramping adventure. This includes the one-day Tongariro Crossing!!! Please make sure that you have clothing to suit the conditions and remember that just because it is sunny and warm when you start does not mean it will remain that way at the top of a mountain. People, usually tourists, die every year on New Zealand mountains because the are ill prepared for the changing conditions.
You will need comfortable but sturdy tramping boots with ankle support, wool socks, thermal underwear (top and bottom), polar fleece or wool jumper, wind and waterproof jacket (such as Gore-tex), gloves, hat, trousers (not jeans) and shorts. If you are camping on the mountain make sure you have a warm sleeping bag and in most cases you will need to carry your own food and sometimes cooking equipment too.
Make sure you check with the local Department of Conservation office (usually located in the Information Centre) as they will be able to give you specific advice for the rotue you are taking.
Make sure you check the weather before you go and pack for every possible contingency.
We started in mild weather, ended up not being able to see further than the end of our fingers, misty cold and had every possible piece of clothing and headgear on but ended up in shorts and t-shirts on the downhill side.
This site might be useful and check before you set out.
Overall this is a very safe walk as long as you are prepared, you need the correct footwear, warm clothes for rapid weather changes, reasonable ammount of fluids.
Take care as it is a difficult area to get rescue helicopters in.
The photo is near the Red Crater and what I thought was the only dangerous part and you guessed it I slipped, but with nothing to grab and a reasonable drop my boots got grip, so I can continue my story.
The night after I did this hike TV ran a story on the dangers of this walk, but only due to people walking in jandals, take it seriously and enjoy.