At the moment there is way of getting Snapchat on Windows mobile. Microsoft has deleted all third party, non official Snapchat apps from their Windows phone store. They did this after Snapchat indicating that they would start “cracking down” on all unofficial Snapchat apps in an attempt to increasing security around their service.
According to a Snapchat they were concerned about how some of the creators of the Snapchat alternatives had build services that could compromise the user’s security. This statement was released after Snapchat recently getting some heat from security experts claiming that Snapchat isn’t taking the user’s security and integrity seriously.
At the moment there is no way to run Snapchat on a Windows phone