Is there any incentive to sleep with a bedroll?

[Splendor]

Possible problems with no bedroll:

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Natural Healing

With a full night's rest (8 hours of sleep or more), you recover 1 hit point per character level. Any significant interruption during your rest prevents you from healing that night.

Being cold or uncomfortable all night long would be a significant interruption.

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Cold

An unprotected character in cold weather (below 40° F) must make a Fortitude save each hour (DC 15, +1 per previous check) or take 1d6 points of nonlethal damage.

For Spellcasters you also have to consider:

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Rest

To prepare his daily spells, a wizard must first sleep for 8 hours. The wizard does not have to slumber for every minute of the time, but he must refrain from movement, combat, spellcasting, skill use, conversation, or any other fairly demanding physical or mental task during the rest period. If his rest is interrupted, each interruption adds 1 hour to the total amount of time he has to rest in order to clear his mind, and he must have at least 1 hour of uninterrupted rest immediately prior to preparing his spells.

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Preparation Environment

To prepare any spell, a wizard must have enough peace, quiet, and comfort to allow for proper concentration. The wizard's surroundings need not be luxurious, but they must be free from distractions. Exposure to inclement weather prevents the necessary concentration, as does any injury or failed saving throw the character might experience while studying.

[Rest] Will sleeping on the hard ground wake you up at night? If so you need to stay in bed longer to be able to regain spells. And my not regain HP at all.

[Environment] You can't prepare spells if its raining on you.

[Sickness] Without proper protection you may have to make fort saves to avoid becoming sick.

Now a simple endure elements will eliminate almost all of these, but then you're short a 1st level spell. Add a umbrella or a tarp (and a light source) and you don't have to worry about the rain.

Rope trick doesn't help until you are at least 8th level (or have a way to extend the spell at 5th). But then you're using up a 3rd level spell.

At lower levels a wizard you really should have a pack mule that carries a bed roll, blanket and a tent for you.

Mule + Horse Blinders + Pack Saddle + Bedroll + Winter Blanket + 1 person tent costs less than 25 gold. Better than wasting a 1st level spell everyday (and the mule's light carry is 100lbs).
Is 100lbs not enough? Upgrade to a yak; 24 gold and it's light carry is 1038lbs.