The issue is not that you can analyze 64-bit dump from 32-bit WinDbg you can. From the WinDbg help file:
If you are analyzing a dump file, and if the dump file was made on Windows XP or a later version of Windows, you can use either the 32-bit package or the x64 package. (It is not important whether the dump file is a user-mode dump file or a kernel-mode dump file, and it is not important whether the dump file was made on an x86-based or an x64-based platform.)
If you are analyzing a dump file, and if the dump file was made on Windows 2000 operating system, you should use the 32-bit package. (It is not important whether the dump file is a user-mode dump file or a kernel-mode dump file)
If you are performing live kernel-mode debugging, and if the target computer is running Windows XP or a later version of Windows, you can use either the 32-bit package or the x64 package. (This situation applies to both x86-based and x64-based targets.)
If you are performing live kernel-mode debugging, and if the target computer is running Windows 2000, you should use the 32-bit package.
If you are performing live user-mode debugging, use the x64 package for debugging WOW64 with both 64-bit and 32-bit code. To debug other targets, use a 32-bit debugger to debug 32-bit code.
What is the issue? Here you are trying to load a 64-bit extension to analyze the problem. It is not possible to load 64-bit extensions on 32-bit WinDbg. The question would then be does the 32-bit version of SOS support 64-bit analysis, can you force WinDbg to use the 32-bit SOS?
You can force a specific version of SOS to load by using
.load as per http://msdn.microsoft.com/en-us/library/bb190764.aspx
However I expect the 32-bit version wouldn't work to analyze a 64-bit process, haven't tried this though.