A very nice intro to Markovian chains

Example 11.1 According to Kemeny, Snell, and Thompson, the Land of Oz is blessed by many things, but not by good weather. They never have two nice days in a row. If they have a nice day, they are just as likely to have snow as rain the next day. If they have snow or rain, they have an even chance of having the same the next day. If there is change from snow or rain, only half of the time is this a change to a nice day.

[...]

We shall be particularly interested in the state of the [... the weather in Oz] after a large number of steps.

How can we model and solve this nice problem? ;)