Are precipitations exothermic and/or endothermic?
No, absolutely not.
Precipitation reactions can be either endothermic and exothermic.

Table 1. Thermodynamic data of precipitation for some salts
\begin{array}{cccccc}
\hline
\text{Salt} &amp; \Delta G_\text{ppt}^\circ &amp; \Delta H_\mathrm{ppt}^\circ &amp; -T\Delta S_\mathrm{ppt}^\circ(\pu{25 °C}) \\
\hline
\ce{Be(OH)2} &amp; -121 &amp; -31 &amp; -90 \\
\ce{Mg(OH)2} &amp; -63 &amp; -3 &amp; -61 \\
\ce{Ca(OH)2} &amp; -28 &amp; 16 &amp; -44 \\
\ce{Li2CO3} &amp; -17 &amp; 18 &amp; -34 \\
\ce{MgCO3} &amp; -45 &amp; 28 &amp; -74 \\
\ce{CaCO3} &amp; -48 &amp; 10 &amp; -57 \\
\ce{SrCO3} &amp; -52 &amp; 3 &amp; -56 \\
\ce{BaCO3} &amp; -47 &amp; -4 &amp; -43 \\
\ce{FePO4} &amp; -102 &amp; 78 &amp; -180 \\
\hline
\end{array}

It is more than clear that all precipitations are not exothermic.

Also definitely noticable is the fact that $\Delta S$ is a positive quantity.

But that is unexpected, as an increase in the disorder of the system upon precipitation may seem counterintuitive to many.

What is often overlooked is that several other factors are at work.

Paving the way

Ions can be of two types:


Electrostatic structure breakers
Electrostatic structure makers


This classification is based on how ions interact with water.

Electrostatic structure breakers

Sometimes referred to as chaotropic ions, these disrupt the hydrogen bonding interactions between water molecules. Examples include $\ce{NH4+}$, $\ce{Cs+}$, $\ce{Br-}$, $\ce{I-}$.

It is tempting to assume that large cations with higher possible coordination numbers would attach and order water molecules more effectively than small cations, but this is not experimentally observed. 

Smaller the radius and/or greater the charge (the more acidic or basic the ion), the greater its structure-making properties in aqueous solution. It is hence clear that the above mentioned ions are structure breakers rather than makers, evidently having very low values of $Z/r^2$.

It is easy to deduce that upon their introduction into aqua, they will correspond to an increase in entropy.

Electrostatic structure makers

AKA kosmotropic ions, these increase the ordering of water. $\ce{Fe^2+}$, $\ce{Al^3+}$, $\ce{Mg^2+}$, are members of this club.

These ions have large charges and relatively smaller radii, resulting in a higher $Z/r^2$ value.

Via hydrogen bonding these ions create relatively larger shells of hydration than their low $Z/r^2$ counterparts.



The differences in hydration for the two types of ions is visible in the following table.

Table 2. Hydration data for some cations


Uh..What does this have to do with the question?

Everything.

The reason that most acidic cations and basic anions combine to give precipitates is due to the disorder that results from the release of large number of water molecules from the well structured hydration spheres.

The second law favours this.



For an example, let us consider the precipitation of $\ce{MgCO3}$

$$\ce{Mg(H2O)36^2+ + CO3(H2O)28^2- &lt;=&gt; MgCO3(s) + 64 H2O}$$

The number of water molecules are derived from Table 2.
The release of $64$ molecules of water per molecule of magnesium carbonate precipitated is very indicative of the positive entropy of the process.

Now for the enthalpy.
Rather than the Gibbs–Helmholtz, let's return to the good old Hess law.

According to Hess' law,

$$\Delta H_\mathrm{ppt}(\ce{M_yX_m)}) = -y\Delta H_\mathrm{hyd}(\ce{M^m+})- m\Delta H_\mathrm{hyd}(\ce{X^y-}) + U(\ce{M_yX_m})$$

The electrostatic structure makers (type 1) would have higher negative

$$y\Delta H_\mathrm{hyd}(\ce{M^m+})+ m\Delta H_\mathrm{hyd}(\ce{X^y-})$$

leading to an overall positive heat of precipitation. e.g. $\ce{FePO4}$, $\Delta H_\mathrm{ppt} = \pu{+78 kJ/mol}$

Vice-versa for type 1: the structure breakers.

I hope I managed to enlighten you on this matter.

P. S. This was a great question. Pardon the short conclusions, I am currently travelling. Members of the community may feel free to edit and make a more dramatic exit.



References:

Hanzlik, R. , Inorganic Aspects of Biological and Organic Chemistry 1976, II, 26-30 

https://www.wou.edu/las/physci/ch412/ppt2.htm

https://www.wou.edu/las/physci/ch412/pptrxn.html