I am running into almost same issue where i need to show exchange calendar of everyone in SharePoint.
If you just want to show the exchange calendar events timing, then probably the Calendar Overlay in SharePoint is the best approach for you. But it will show the event time and the status i.e Busy, Free, In Meeting etc not the actual event detail i.e Meeting with Boss, Annual Dinner etc. Only one's own exchange calendar will be visible to him after login into SharePoint. No one else can see other's calendar. Below is the guide to setup Calendar Overlay.
The other method is using custom code development. You can write some custom code to query the exchange server with any valid login ID to get Calendar events. You can use impersonation in code and then can query anyone's exchange Calendar. For implementing impersonation, you would need a service account that would have read access on all exchange calendars. Below is a sample web part that fetches emails from exchange by implementing impersonation. You can modify the code according to your requirements.
Hope it helps.