For natural $n$, let $$U_n:=\{x=(x_1,\dots,x_d)\in C_0([0,1];\mathbb{R}^d)\colon \Phi(x_1(1))\in\delta_n\}, $$ where $\Phi$ is the standard normal pdf and $\delta_n:=(1-1/2^{n-1},1-1/2^n)$. Then the family $(U_n)$ has all the desired properties.

For natural $n$, let $$U_n:=\{x=(x_1,\dots,x_d)\in C_0([0,1];\mathbb{R}^d)\colon \Phi(x_1(1))\in\delta_n\}, $$ where $\Phi$ is the standard normal pdf and $\delta_n:=(1-1/2^{n-1},1-1/2^n)$. Then the family $(U_n)$ has all the desired properties.

Indeed,

(i) for each natural $n$, the set $U_n$ is open, because $\delta_n$ is open;

(ii) the $U_n$'s are disjoint, because the $\delta_n$'s are disjoint;

(iii) $$\nu(U_n)=P(\Phi(B(1))\in\delta_n)=1/2^n, $$ where $B$ is the standard Brownian motion -- because $\Phi(B(1))$ is uniformly distributed on $(0,1)$;

(iv) the property $\nu(C_0([0,1];\mathbb{R}^d)-\cup_{n\in\mathbb{N}} U_n)=0$ follows immediately from (ii) and (iii).