The only proper hotel that is open round the year is Shalimar Hotel ziarat. There are other hotels which are closed but the watchmen can open it for you on charge . These hotels do not have basic facilities like hotwater,heater and restaurant etc so the stay in these hotels is not advisable. The roads are usually open unless there is heavy snowfall. The recent snowfall will be washed way by the time you reach there. So probably you can reach ziarat.
The bus route is faster than train but if you can afford then go for private car. The rental cars service from karachi to quetta is available from old subzimandi they have toyota corrolla. From quetta one can either hire a private car or travel by hiace vans both are available at Pishin adda.
Hope this helps.
Can any one reply to my thread regarding abbotabad,balakot,nathia gali