For certainty, ask your supplier if their home heating fuel oil was from the same tank as: No.2 Diesel.
"Typically", home heating fuel oil for indoor basement tanks is the same as No.2 Diesel fuel. This is "summer" diesel.
In my opinion there are a couple issues here: 1) Can fuel oil be stored outdoors in tractor's tank in colder weather? 2) Lubricity for tractor fuel pump.
I also don't know enough about low sulfur vs high sulfur diesel and/or fuel oil, but I don't think this is an issue anymore. I'll let others comment.
No.2 diesel fuel can gel at temps below 40 degrees, so "winter" diesel sold at stations or delivered for trucks/tractors is often a mix of No. 1 & No. 2 Diesel, and/or may have some anti-gel additives. If your furnace fuel oil tank is outside, your fuel oil may also be a mix of No.1 & No.2 diesel. This is fine for diesel motors.
If your fuel oil is straight No.2 diesel, add a anti-gelling treatment (Power Service white bottle) to it if you have cold temperatures.
To be on the safe side, I'd add some diesel treatment to help fuel pump lubricity (Power Service grey bottle) too in case there is some difference in supplier's "diesel" vs. "fuel oil". It won't hurt.
And if you do nothing, that would probably work too. (i.e. none of this is probably a big deal)