According to what I find, the perhaps most straightforward way of achieving this is to employ pic
s.
\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{decorations.fractals}
\tikzset{pics/.cd,
snowflake/.style n args={2}{code={%
\begin{scope}[decoration=Koch snowflake]
\draw[#1] decorate{decorate{decorate{decorate{(-1.5,1) -- (1.5,1)}}}};
\draw[#1] decorate{decorate{decorate{decorate{(1.5,1) -- (0,-2)}}}};
\draw[#1] decorate{decorate{decorate{decorate{(0,-2) -- (-1.5,1)}}}};
\path[#1] (-1.5,1) -- (1.5,1) -- (0,-2);
\node at (0,0) {#2};
\end{scope}}}}
\begin{document}
\begin{tikzpicture}[scale=.6,auto=right]
\pic[local bounding box=n6,scale=0.3] at (31,20) {snowflake={fill=yellow}{6}};
\pic[local bounding box=n4,scale=0.3] at (34,18) {snowflake={fill=yellow}{4}};
\pic[local bounding box=n5,scale=0.3] at (38,19) {snowflake={fill=yellow}{5}};
\pic[local bounding box=n1,scale=0.3] at (41,18) {snowflake={fill=yellow}{1}};
\pic[local bounding box=n2,scale=0.3] at (39,16) {snowflake={fill=yellow}{2}};
\pic[local bounding box=n3,scale=0.3] at (35,15) {snowflake={fill=yellow}{3}};
\foreach \from/\to in {n6/n4,n4/n5,n5/n1,n1/n2,n2/n5,n2/n3,n3/n4}
\draw (\from) -- (\to);
\end{tikzpicture}
\end{document}
The cleanest way would probably be to define a new shape. Given the complexity of the shape, this might not be straightforward, but it is conceivable that it is not impossible. Another option would be to use a path picture of a node, but like in the pic
s above that would "only" lead to background pictures and in particular not define the boundary of the nodes, meaning that the gaps in the lines connecting the snow flakes would be similar to above. (They may become slightly smaller if you base the node on a circle shape, but path pictures have other subtleties which is why I removed this part of my earlier answer.)
Note that, if you are concerned about the gaps in the lines connecting the nodes, there is a simple fix.
\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{decorations.fractals,backgrounds}
\tikzset{pics/.cd,
snowflake/.style n args={2}{code={%
\begin{scope}[decoration=Koch snowflake]
\draw[#1] decorate{decorate{decorate{decorate{(-1.5,1) -- (1.5,1)}}}};
\draw[#1] decorate{decorate{decorate{decorate{(1.5,1) -- (0,-2)}}}};
\draw[#1] decorate{decorate{decorate{decorate{(0,-2) -- (-1.5,1)}}}};
\path[#1] (-1.5,1) -- (1.5,1) -- (0,-2);
\node at (0,0) {#2};
\end{scope}}}}
\begin{document}
\begin{tikzpicture}[scale=.6,auto=right]
\pic[local bounding box=n6,scale=0.3] at (31,20) {snowflake={fill=yellow}{6}};
\pic[local bounding box=n4,scale=0.3] at (34,18) {snowflake={fill=yellow}{4}};
\pic[local bounding box=n5,scale=0.3] at (38,19) {snowflake={fill=yellow}{5}};
\pic[local bounding box=n1,scale=0.3] at (41,18) {snowflake={fill=yellow}{1}};
\pic[local bounding box=n2,scale=0.3] at (39,16) {snowflake={fill=yellow}{2}};
\pic[local bounding box=n3,scale=0.3] at (35,15) {snowflake={fill=yellow}{3}};
\begin{scope}[on background layer]
\foreach \from/\to in {n6/n4,n4/n5,n5/n1,n1/n2,n2/n5,n2/n3,n3/n4}
\draw (\from.center) -- (\to.center);
\end{scope}
\end{tikzpicture}
\end{document}
I am, of course, not claiming that the lines hit the "nodes" precisely in the same way as \pgfpointshapeborder
would, but since these snow flakes are sort of spherical, it almost works.
ADDENDUM: as requested in the comments, a version with 3 arguments, where the 3rd argument are the node options such as color, font etc.
\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{decorations.fractals,backgrounds}
\tikzset{pics/.cd,
snowflake/.style n args={3}{code={%
\begin{scope}[decoration=Koch snowflake]
\draw[#1] decorate{decorate{decorate{decorate{(-1.5,1) -- (1.5,1)}}}};
\draw[#1] decorate{decorate{decorate{decorate{(1.5,1) -- (0,-2)}}}};
\draw[#1] decorate{decorate{decorate{decorate{(0,-2) -- (-1.5,1)}}}};
\path[#1] (-1.5,1) -- (1.5,1) -- (0,-2);
\node[#3] at (0,0) {#2};
\end{scope}}}}
\begin{document}
\begin{tikzpicture}[scale=.6,auto=right]
\pic[local bounding box=n6,scale=0.3] at (31,20) {snowflake={fill=yellow}{6}{text=red}};
\pic[local bounding box=n4,scale=0.3] at (34,18) {snowflake={fill=yellow}{4}{font=\sffamily,text=blue}};
\pic[local bounding box=n5,scale=0.3] at (38,19) {snowflake={fill=yellow}{5}{rotate=45}};
\pic[local bounding box=n1,scale=0.3] at (41,18) {snowflake={fill=yellow}{1}{}};
\pic[local bounding box=n2,scale=0.3] at (39,16) {snowflake={fill=yellow}{2}{}};
\pic[local bounding box=n3,scale=0.3] at (35,15) {snowflake={fill=yellow}{3}{}};
\begin{scope}[on background layer]
\foreach \from/\to in {n6/n4,n4/n5,n5/n1,n1/n2,n2/n5,n2/n3,n3/n4}
\draw (\from.center) -- (\to.center);
\end{scope}
\end{tikzpicture}
\end{document}