Since I'm back home with a full size keyboard I'm going to jump in this thread too
...and say that the time you have available to do these tasks is the driver for the size & hp of the of the tractor (hp and size can be very different things).
For example mowing, how much of the acreage are you going to keep mowed as a lawn/yard? How often will you be mowing it and how much time do you have to mow it? This would drive the size of the mower you'll want/need which in turn will drive the PTO hp. I wouldn't recommend going below 5hp per foot of mower width, and I wouldn't count on being able to go faster than 3-5mph unless you plan on making your yard golf course smooth and keeping it that way. BTW you'll also want to compare where the prices of MMM vs. 3pt finish mowers vs. standalone mower end up as there can be some very distinctive price differences at different sizes. For example a quality 72 inch 3pt finish mower can be much less expensive than a similarly sized MMM or independent mower. There can be a bit more of a learning curve with a 3pt mower, but having had MMM and zero-turns I'd say it also has it's own distinct advantages as well ..... higher lift heights and not being between the wheels being a couple.
Likewise if you look around you'll probably be able to find some recommendations on hp per foot of working with for snowblowers, and you'll probably want to go with one that covers the width of the tractor -- not necessarily a requirement to cover the tractor width, but .....can make things a bit easier. Depending on the amount and type (powder vs slush) of snow you get snow pushers or blades may be a preferable alternative. Large amounts of wet snow will require more hp to move at the same width & speed as a dryer/powdery snow. That may not be as much of an issue with newer tractors, but with older ones you may run into an issue of not having enough hp at the PTO to make a snowblower worthwhile.
Unless your property is free of rocks and roots I wouldn't recommend a PTO auger (unless of course you're a glutton for punishment). Been there done that and 20 years later still remember how much of a nuisance it was to free a PTO auger after it'd caught on an underground obstruction and had to be freed by hand. Suggest either renting a skid steer with a hydraulic auger or getting a tractor that can run one on the loader (the down pressure and ability to reverse the auger can be good things - especially in challenging soil conditions).
Tilling would also fall into the same thought process as mowing - though the hp per foot of width will be different (more tends to be better). Of course when it comes to working the ground the method chosen can change the characteristics of the tractor you'll want .... PTO driven implements will drive more HP, and draft implements like plows, disk harrows, etc will want more effective draft hp (which is usually limited by the weight of the tractor).
Things to consider for the loader are what heights will you need to reach and at what distances? ....and what sort of unbreakable loads will you need to lift? For example my criteria was based off of 55 gallon drums of water (which are roughly 400-500lbs each when full) ...and don't forget the weight of the attachment/implement as the loader will still need to lift that weight too.
That leads to considering any other hard limits as far as height and width of the tractor itself along with if any tasks may call for specific options on the tractor. There's the obvious 3rd function on the loader for using grapples, but rear implements with hydraulics can also make life easier (top & tilt kits, hydraulically angled rear blades or snowblower chutes)... and of course there's always the cab vs open station consideration (which for most goes cab as soon as snow removal or extreme become a consideration).
All of those things are what should be balanced against the budget you have -- where I'd suggest looking at the budget from not only total cost but monthly costs as well (since that's usually how many payments are made).
The thing to remember when looking at tractors is the tractor is a carrier and power source and it's the implements (front and rear) that are doing the work. So look at the implements you may eventually want/need to use and how quickly you'll want/need to complete the tasks you'll be using them for and let that drive your tractor sizing.....
Apologies for the length of this, just wanted to cover the different tasks mentioned and tweak the perspective of how to look at tractor sizing/buying process ....as I'd wager most early trade-ins are based upon individuals buying a tractor based on HP rather than sizing it for the tasks the buyer wanted to do.....
