https://www.diyspareparts.com/parts/mountfield/diagrams/1430/05d6f7b9-0cc5-4328-bf3b/
I’ve done it on several Murray mowers with a hydrostatic transmission, and the parts diagram above looks very similar. Access is much easier if you remove the cutting deck (5 minute job) and you can then prop it up on a big block of wood or something.
Some limited disassembly will be required but I don’t recall anything scary. Everything else is pretty easy if you follow the diagram, though make sure the belt is running on the guide/tensioner pulleys and not over any of the anti-throw pillars because it’s not totally obvious at times.
Pretty sure you can do it without dropping the engine pulley though you might need to disconnect the steering rack or brake pedal.
Edit: it’s actually quite hard to snap a drive belt twice so may be worth checking things over while it’s apart. Avoid shock loading the gearbox (using the reverse portion of the gearbox as a brake, for example) and look for obvious wear in the drive or gearbox pulleys, which can overheat the belt.