Insulating bedroom w/half vaulted ceiling...?

Based on your description, it sounds like the room may be losing heat through a combination of the vaulted ceiling, the large window area, and possibly limited airflow from the HVAC system due to its location furthest from the furnace. In most cases, improving the insulation and air sealing of the vaulted ceiling is a better long-term investment than continuing to rely on a space heater. Electric heaters can help make the room more comfortable, but they don't address the underlying issue and can become expensive to operate over time. Vaulted ceilings can be challenging because there is often less space available for insulation than in a conventional attic. Depending on how the roof was constructed, options may include adding spray foam insulation, increasing insulation levels during a renovation, or improving ventilation and air sealing within the roof assembly. The wall of windows is also worth investigating. Older windows or failed seals can contribute significantly to both winter heat loss and summer heat gain. In some homes, upgrading windows or improving weatherstripping can make a noticeable difference in comfort. As for costs, they can vary considerably depending on accessibility and the insulation method used. Smaller upgrades such as air sealing may cost a few hundred dollars, while opening up a vaulted ceiling and upgrading insulation can range into the thousands depending on the scope of work. A thermal imaging inspection or energy assessment can often identify exactly where the heat loss is occurring and help determine which improvements will provide the greatest return on investment. In our experience, addressing the building envelope almost always delivers better comfort and efficiency than simply adding more supplemental heat.