Download Oracle Database 10.2.0.4 For Windows Download Portable
Technically, yes — with compatibility modes and manual adjustments (Oracle services might fail to start). But it is neither certified nor recommended. Use a virtual machine with Windows Server 2008 R2 for reliable operation.
For licensed customers, the most reliable way is to log into My Oracle Support and open a "Software & OS Media Request". Oracle Database 10.2.0.1 (the base release) first. Once the base is installed, you can download and apply the 10.2.0.4 Patch Set from the "Patches and Updates" tab in MOS. Oracle Software Delivery Cloud: Valid license holders can check the Oracle Software Delivery Cloud Download Oracle Database 10.2.0.4 For Windows Download