I've checked the official website and it appears that you can use Microsoft Visio 2010 on Windows 7 because it's a supported operating system. As you can see below, I've pasted the versions of Windows that are compatible with Microsoft Visio Viewer 2010.
System requirements: Windows 7, Windows Server 2003 R2 (32-Bit x86), Windows Server 2003 R2 x64 editions, Windows Server 2008 Service Pack 2, Windows Vista Service Pack 1, Windows Vista Service Pack 2, Windows XP Service Pack 3.
For additional downloads and information, check the page provided by Microsoft.
