You're correct that a headwind will reduce the takeoff roll (takeoff distance). As far as takeoff speed, the airspeed will remain same, but the ground speed will be reduced.
In the simplest sense, an aircraft rotates for takeoff when it generates enough lift (leaving aside other considerations). This is dependent on the airspeed as the lift generated is propotional to the square of airspeed (provided the other factors like wing area and lift coeffecient are kept constant) at a density altitude. As a result, it is the airspeed, not the groundspeed that matters.
If you have some headwind, the effective groundspeed is reduced by the same amount- resulting in reduced takeoff distance. The effect of the wind on landing distance is similar to the takeoff distance. You can see this in the following figure.
Image from avstop.com
As it can be seen, the presence of winds can have a significant effect on the takeoff disantances required (note that the airspeed remains the same in all cases). Due to this, the direction of prevailing winds can have a significant effect on determining the runway headings. From Influences on Airport Layout:
The weather patterns of an area, especially the prevailing winds, are a major factor in determining runway headings. Prevailing winds are defined as the direction from which the winds blow most frequently. Remember that airplanes take off and land into the wind. Let's say that at a given airport the prevailing winds blow in from the west 65% of the year, while 30% of the year the wind blows in from the east, and the remaining 5% coming from the northwest. It would be best then to orient the runway W (27) and E (9). That would mean that approximately 95% of the year airplanes would be landing and taking off into the wind.