If it will be done the same way war on drugs is done, people would be put into jail for mandatory minimum sentences for failing to register their home address with the police and for being on the streets while the curfew is in place. Any "precursor" materials such as warm clothes, tents, hiking boots, survival guides, etc. and hiking would be illegal (a teacher probably would be fired on spot for just suggesting the students to have an outdoors trip). Any outdoors activities which involve staying outside past curfew time will have to be issued a permit from the police, and only people passing special extensive anti-homelessness training would be allowed to possess such permits. Places where homeless people could find shelter would be destroyed by the police or rendered uninhabitable at huge expense and use of toxic and lethal material (inevitable deaths following that would be dismissed as acceptable collateral damage). Anybody seen helping a homeless person with money or food or anything else would be also subject to arrest and felony conviction. Of course, the police would also involve massive amount of undercover agents to trick people into doing exactly that and later bust them for aiding and abetting the homelessness.

In short, if you want war - it would be a war. And war is not pretty. Especially when the government declares the war on its own citizenry.