Since then, residential areas, Queens Park, the railway tracks, green spaces and the Otepuni Stream had been searched, some more than once.
Sgt Martin said the search had involved dog handlers and kayakers going down the stream.
"There is nothing to indicate he is outside the area."
Those involved were extremely concerned for his welfare, given the temperature dropped to 1.3degC on Tuesday night, Sgt Martin said.
That concern led to the decision to send an emergency alert to those in the Invercargill area on Tuesday night.
About 8pm, the alert, similar to the Covid-19 alert, informed Invercargill residents Horn was missing. It also advised people to look around their properties.
Sgt Martin said the black and red jacket Horn was thought to be wearing could be similar to a Honda jacket.
Police said he could also be dressed in a light-coloured polo shirt, gym shoes and sweatpants or jeans.
Invercargill residents were asked to search their properties, even if they have previously searched them, as Horn was believed to be on foot and might have wandered on to a property.
Sgt Martin said it would be helpful for anyone with CCTV on their properties to review the footage and submit it to police if they saw anyone who looked like Horn.
A crew of 12 Land Search and Rescue volunteers were involved yesterday, as well as members of Amateur Radio Emergency Communications group who were working with the incident management team.