That's a tough call.
Reasons Oil Could Go Higher
>Worsening of the Ukraine war. E.g. another assault from Belarus, attacks on peripheral countries, sabotage of infrastructure, a total war declaration by Russia, etc.
>China emerges from zero-COVID and their economy starts heating up
>Years of insufficient E&P investment by oil companies is catching up with demand growth
>Typical pre-recession burn-up in prices
>European hoarding gets desperate
Reasons Oil Could Go Lower
>Fossil fuels usually tank as a recession starts and a lot of demand dries up.
>A Chinese + European recession
>OPEC+ reaches a deal to sell more oil, or members oversell their quotas
I would be tempted to buy now, but you could hedge either decision. If you wait, the risk is that oil goes from $4.47 to let's say $8 by the time you buy. That's going from $2,235 to $4,000, an increase of $1,765 or 79% in that scenario. If you wanted to wait, you could hold $2,235 worth of USO shares until your oil purchase date. If the price of oil goes up between now and then, the rise in USO will very-roughly compensate you for the higher price you must pay, before taxes. Likewise, if you buy now but want to avoid regrets in case the price of oil drops later, you could buy put options on USO. The details of exactly which options and how many can be tough to work out, but probably if you controlled $3k worth of shares that would be roughly sufficient.
A simpler choice might be to purchase half your oil now and half later, obtaining the average price between those time periods. However I'm sure there are delivery charges to consider.
Obviously, the low-hanging fruit here is to add insulation to your house, caulk up any gaps, shrink-wrap plastic over the windows or build storm windows, refresh the seals on your doors, etc.
Regarding the mini-split idea (or other electric heat sources) maybe come up with a cost-per-BTU estimate to heat your house in terms of kWh or gallons of oil. There will be a breakeven point where electricity and a heat pump are cheaper than the oil furnace. Then choose your method accordingly.