There is no objective that asks you to send a horse to heaven. However sending it to safe haven is an objective that can be asked for.

A horse will go to heaven when its health goes below a certain level. So you must actively starve that horse of any of the care activities over a period of time to do so.

The horse simply needs to die. Once dead you have the option to revive it (if it's not older than 25 years (30 years with Midas' VIP bonus) or send it to heaven and your Yggdrasil will age

There is no such place as 'Safe Heaven'....! It is Safe HAVEN.... a sanctuary for unwanted horses...

Whereas Heaven is where horses can be sent when they die.

To kill a horse quickly, you need to work it (Rides/training/comps) so that it's energy drops below 5%, and also do no care actions (including grooming), just bed it.

You might need to repeat this for two or three agings if it was fully healthy at the start. Then, when it dies, follow Eleyii's advice on how to send it to Heaven

Ah ok not sure why it didn't work for the objective then that's weird I thought I'd read it wrong. I'll try again lol. And thankyou for your helpful advice